Archive of changes made during September 2009. The substantive content of this page should not be altered. The announcement of the change to the Forum and the reasons for it have been archived.
Urs Schreiber: created blob homology
Added a ‘blink (= stub-link) at higher order proposition.
Added a quote to precursors in which Hilbert borrows an idea from Kant.
added the example of automorphism 2-groups to 2-group
added reference to the new article by Batanin, Cisinki and Weber to generalized Gray tensor product – Mike, did you look at that?
Toby Bartels: More at SEAR+??.
Mike Shulman: Toby is right?.
Zoran ?koda?: entry internal crossed module.
Zoran ?koda? created general linear group.
Toby Bartels: I'm pretty sure that SEAR+?? satisfies $COSHEP$.
Todd Trimble: created PRO, and began (re)adding material to cube category, with a view toward incorporating material from the Grandis-Mauri paper on cubical sites. Discussion with David Corfield at cubical set.
Urs Schreiber: added the example of “derived schemes with $E_\infty$-ring”-valued structure sheaves to generalized scheme.
Zoran ?koda? separated Lurie material, with a link from scheme to scheme as locally affine structured (infinity,1)-topos.
Urs Schreiber: thanks, Zoran. I have renamed the entry to say $(\infty,1)$-topos, as I think we agreed to be (more) careful than Lurie is about this.
Urs Schreiber: added the alternative definition in terms of sheaves on $Aff/X$ to quasicoherent sheaf.
Urs Schreiber expanded the definition at scheme:
added a word on the definition of morphisms, gave the sheaf-theoretic version and the definition from the derived scheme perspective. In that context I cited the full paragraph of Jacob Lurie where he argues that the standard definition is misleading in that it asserts an underlying topological space, and that one better thinks of a scheme as having an underlying locale/0-topos.
Urs Schreiber: sure, let’s split off sub-entries when it gets too long. You are currently locking the entry, otherwise I would have done it.
Zoran ?koda? changes to generalized scheme.
part 3 at A Survey of Elliptic Cohomology - E-infinity rings and derived schemes – in that context also created: Paul Goerss, n-truncated structured (infinity,1)-topos, Spectral Schemes, Topological Algebraic Geometry - A Workshop
stub entry for derived scheme and derived Deligne-Mumford stack
have two questions (green query boxes) at algebraic stack
moved the Deligne-Mumford reference from algebraic stack to Deligne-Mumford stack
created brief entries on representable morphism of stacks and geometric stack, but that needs attention
added to affine space a section “Affine spaces as model spaces”.
more details at geometry (for structured (infinity,1)-toposes)
David Corfield: Carried on the discussion at cubical set. Now we need to decide whether Pratt’s use of the term is sufficiently widespread to justify disambiguation.
more details at generalized scheme
edited derived algebraic geometry (a bit structuring by headlines and some paragraphs here and there)
Mike Shulman: A reference at COSHEP.
Mike Shulman: In response to the discussion at choice operator, I started SEAR+?? about whether and why adding a non-extensional choice operator is a conservative thing to do to a theory that lacks AC. So far I can prove that it is conservative over COSHEP.
Added potentially enlightening quotes from Hilbert and Ackermann to precursors. Better lights might be thrown by the original German or the first edition — all I have on hand right now is the English translation of the second edition.
Added a historical note to choice operator.
Zoran ?koda? created entries affinoid algebra, rigid analytic geometry (just started), derived noncommutative geometry, unique factorization domain.
a couple of queries at cubical set.
Urs Schreiber I don’t know the answer to the first question. Concerning the second: the answer to questions of the form “shouldn’t we do …?” is usually: “yes, we should, why don’t you go ahead and do so?”
Todd Trimble took a crack at addressing queries.
added a remark on Connes’ program to noncommutative geometry, but still no genuine content
started adding details to generalized scheme
two formatting problems:
the MathML in the headlines makes the TOC have too much vertical spacing
the hyperlinks in the definition/theorem names don’t appear as such (I think they used to work there in the old setup)
I leave it typeset this way anyway, trusting that we can eventually fix the software instead of working around it
worked on noncommutative algebraic geometry: added lots of links (many to existing entries, some to entries that ought to be created eventually), added more sections and a table of contents, then I expanded the Idea section, trying to give a better idea to laymen. Please check!
Jon Awbrey spun off the speculative archaeology of category theory to its own page at precursors.
Zoran ?koda? changes to generalized scheme.
Urs Schreiber added material to cubical set (on relation to homotopy theory), that Ronnie Brown had posted to the Alg-Top mailing list
Todd Trimble: added commentary to Rafael’s suggestion at category theory, at the end of the penultimate discussion box.
Urs Schreiber created exterior differential system and related to that dg-ideal and vertical tangent Lie algebroid
Toby Bartels: Sorry at natural numbers in SEAR.
Rafael Borowiecki: Replied at category theory and suggested changing one of the views what category theory is.
Zoran ?koda? created localized coinvariant, universal localization, noncommutative localization, coinvariant; new links at Zoran ?koda?.
David Roberts: question for Toby at natural numbers in SEAR, in 'alternative approach'.
Toby Bartels: SEAR, pure set, natural numbers in SEAR, category theory, choice operator.
David Roberts: fixed up problem at natural numbers in SEAR pointed out by Mike, and included another, cleaner, definition.
Zoran ?koda?: created universal enveloping algebra, enveloping algebra.
David Roberts: polishing up natural numbers in SEAR. The definition is in, now.
Zoran ?koda?: created Ore localization.
Urs Schreiber: worked on geometry (for structured (infinity,1)-toposes)
expanded and improved “Idea” section
in “References” section started commented list with explicit pointers to definitions
needs expansion – and warning: I think I missed some $(-)^{op}$s and $Ind(-)$s. But have to run now.
Mike Shulman: Some discussion is continuing at pure set.
Urs Schreiber some rough notes on genera and the elliptic genus at elliptic cohomology.
Andrew Stacey: Who’s the emacs guru who put the stuff on the HowTo about using Emacs?
Mike Shulman: I guess that would be me.
Andrew Stacey: Great! I have a forum discussion for you. Of course, anyone else interested in using Emacs for editing nLab pages is welcome to join in.
Ivo? created free groupoid and Urs Schreiber went over it and added links, and typeset math.
Mike Shulman: A different viewpoint on universes in SEAR.
Rafael Borowiecki: Replied at category theory. Now i understand less than i did before.
David Roberts: A bit at Morita equivalence, on the version for Lie groupoids, and a sketchy start to universes in SEAR.
Zoran ?koda? created a rough outline for Ore set and plan to have the entry on Ore localization separate.
Urs Schreiber: created Euclidean supermanifold and worked slightly more on the stub for Clifford algebra
Zoran ?koda? created a rough outline for descent in noncommutative algebraic geometry.
Dmitri Pavlov Asked two questions at the Morita equivalence page.
Andrew Stacey Reorganised the HowTo a little - hopefully haven’t lost any information! - so that the automatic table of contents looks like the old one did (almost).
left some new entries unfinished, but have to resume finishing these later today
added instructions for automatics TOCs to HowTo
some content fed into supermanifold – alse created SDiff, SVect, super vector space, super algebra, Grassmann algebra, super Lie algebra
Jon Awbrey is road-testing the “cylindricity” symbol $\text{⌭}$ (unicode ⌭) for composing functions and relations the right way, that is, in arrow order. For example, see boolean-valued function.
I believe a semicolon $;$ is already commonly used by many people for composing things in “diagrammatic” order. -Mike
Yes, there’s a Z-notation semicolon ⨾ (unicode ⨾) that I tried for a while, but it always looks more like a (California) stop than a connector — besides, Kurt Vonnegut says not to use ‘em.
Urs Schreiber: added automatic TOCs to limit, adjoint functor, Kan extension, cohomology, FQFT, category theory, descent and maybe some other entries
this feature is great! we should insert it in most entries. Even though I was very much involved with all these entries, I was still surprised to see how long and detailed some of these tables of contents are. They really give an impression of a long entry that is not available otherwise.
one entry that really deserves a TOC is category of fibrant objects – but I failed to insert one there. Encountered lots of strange behaviour like truncations of the entry (had to rollbck several times) or error messages after saving. Could it be that this entry exceeds some length limit?
Lab Elf (carpentry division): The length limit is really long now, about 500 million characters. If we get that long we should contact the Guinness book of records. The problem was actually due to having a wiki-link in one of the headings. Oddly enough, there was no error message on this in the logs but changing it solved the problem (it now says “see also fibration sequence” after the heading). I imagine it’s to do with the fact that things in the table of contents are links to the sections in the document so having a wiki-link would mean that one thing (the entry in the table of contents) was a link to two places (the section and the page the wiki-link points to). As the Maruku filter is independent of the wiki, it doesn’t know of wiki-links and so doesn’t know how to handle them.
Mike Shulman: More at SEAR, including how to eliminate equality entirely, and how to prove the SEAR Collection axiom from ZF.
Urs Schreiber: many thanks to Jon Awbrey for providing help with automatic TOCs. Great that it works now, but why does it? What does that funny “tic” thing achieve? Let’s discuss this on the forum – here – and summarize the result at HowTo eventually
Toby Bartels: Working the foundations at SEAR, pure set, and natural numbers in SEAR.
Zoran ?koda? expanded proper map.
now a bit of real content at Brown representability theorem
added link to Iglesias’ PhD thesis to diffeological space – the link to this thesis is hidden somewhere on his website, and it was pointed out to me that the thesis contains some noteworthy material which is not in the book (yet), such as discussion of diffeological principal bundles
Zoran ?koda? added references to Heisenberg double (including my own).
Urs Schreiber wrote very stubby stub for Brown representability theorem, in fact just recording a recent reference there
Lab Elf (carpentry department): Maruku (the implementation of markdown used here) can do automatic tables of contents (for use within a page, it can’t do cross-page contents). For an example see this page and for the syntax, see the maruku extended syntax page.
Urs Schreiber: ah, thanks Lab Elf! I wasn’t aware of this. This will save me a few keystrokes. Should be mentioned at HowTo.
Jon Awbrey tried that at differential logic and couldn’t get it to work. Is there some extra trick to that?
Jon Awbrey: It looks like you have to start your headings with single #‘s and use a flush left tag something like this:
created functorial quantum field theory - contents and added it as a floating table of contents to relevant entries – trusting that the related issues currently discussed on the forum will eventually be solved by CSS means
created stubs for Riemannian manifold, Riemannian cobordism, isometry
added to Gray tensor product a link to Mike’s new generalized Gray tensor product
Replied to several comments at SEAR, and rearranged the discussions to be (mostly) next to the text they are discussing. I’m happy about the interest this idea is generating.
Wrote generalized Gray tensor product about a folklore no-go argument that I keep forgetting and having to re-produce.
David Roberts: comments at SEAR:
suggestion for renaming - SER (and SEPS for Toby’s alternative)
comment about the category of SEAR-sets
the kick-start of a new project, natural numbers in SEAR. This is without assuming the axiom of infinity and otherwise assuming as few of the SEAR axioms as possible. A little over a stub at present, and maybe I’m making a big deal of nothing…
Heated discussion at SEAR.
Jon Awbrey is setting some tables at differential logic.
created stub for supergroup
created geometric models for elliptic cohomology with sub-entries so far:
this comes with this blog entry here
created stub for partition function
created modular form, but this needs more attention
added the promised blurb to directed space under “homotopy theoretic perspective” that is supposed to indicate the idea of the relation to (n,r)-category without misleadingly sounding as if there were nothing left to do here. Check!
I also added links to Grandis’ new book on Directed Algebraic Topology to directed space and to directed homotopy theory. Since I haven’t had a chance to look at that book yet, I have a question at directed space about its content.
David Corfield: Why call the page Directed Homotopy Theory when it’s about a book called ‘Directed Algebraic Topology’? Don’t titles of pages for specific texts coincide with titles of the texts?
Urs Schreiber: I just wondered about the same thing – I made Directed Algebraic Topology now redirect to that entry, but if Zoran is okay with it I would also suggest to rename this. Book entries should carry the title of the book, at least up to abbreviation.
Sorry, I am overloaded in last few days and made an error. Funny enough, there is a historical parallel with russian EGA. Russians have published a translation of the the introduction to 1971 EGAI edition. The external pages says Elements of algebraic geometry, while the title on the very first page is Elements of algebraic topology. I have a scan of this funny “typo”.
Urs Schreiber: restructured moduli space, linked to it from classifying space and, notably, added a semilong discussion of the subtleties of the common slogan that “ Objects with automorphisms don’t have fine moduli spaces . ”, summing up some arguments that were exchanged in the blog discussion here.
Toby Bartels: Reply to Mike at foundations.
Mike Shulman: Rafael, your clarification at category introduced another typo! (-: Now fixed.
Urs Schreiber: quick reaction at (n,r)-category – am still not quite back online, but trying…
Todd Trimble responded to Rafael Borowiecki at category theory.
Toby Bartels: I don't think that those typos in (n,r)-category were typos, but I tried to clarify them.
Zoran ?koda?: new stub K-theory and physics. Book entry Directed Homotopy Theory. Added references to basic ideas of GW.
Zoran ?koda?: new entry Vladimir Drinfel'd. Improvements to Q-category, noncommutative algebraic geometry.
Mike Shulman: Incorporated the discussions at Crans-Gray tensor product into the entry, and deleted them.
David Roberts: Comment/reference at directed homotopy theory - Grandis has a book out now on this stuff.
Arnold Neumaier has joined to talk about SEAR.
Jon Awbrey added some (hopefully) motivating remarks and lots of pretty pictures to differential logic.
Andrew Stacey I’ve disabled the export features. They now redirect to a section of the HowTo which explains how to use wget
to get a local copy of the n-Lab. If anyone wants to add instructions for other programs or OSes then, of course, feel free.
David Corfield: chipped in at (n,r)-category.
Jon Awbrey added more content to differential logic.
Zoran ?koda?: Yuri Manin, Arakelov geometry; small changes to moduli space.
David Roberts: Comments at SEAR. From what I’ve seen, I like it.
branched off the seminar notes mentioned below to basic ideas of moduli stacks of curves and Gromov-Witten theory
in that context created moduli space, currently also being the redirect for fine moduli space, coarse moduli space and moduli stack
all still mighty rough, but I think valuable raw material to base further editorial developments on
Andrew Stacey I have replied to Zoran’s points over on the n-Forum at this discussion since that seems a better place to have a discussion than here.
am taking notes in a seminar on Gromov-Witten theory
started something at deRham theorem
created simplicial sheaf
Zoran: I am strongly against shifting latest changes to the forum. I do not know how to quickly link and do other features like here, it requires more downloading capacity when on expensive network like mobile, it may require account, it does not get recorded when downloading the whole nlab etc etc. Logging to forum is anyway pain when on mobile network. It logges you off for example if you are idle for 30 minutes. I will not do it simply. I quit logging changes if it is to the forum. I will edit nlab without logging changes in that case. Nlab is nlab, and it should be self contained. Forum is about general policies, it is complicated enough to explain to the new userts that there is latest changes notificatiopn, notg in addition now that they have to have an additional account and additional web page with different software. I never use RSS feeds nor want to use them: I do not check latest changes unles sI am generally interested what is there. If I work on the item “jabberwocky” I WORK on it. If I want to see latest changes I look at them. It is very important that I can download the whole nlab including the latest changes histories. Forum is different system and it should not be mandatory to use it. I also find useful that I can link and cut and paste formulas and nlab links easily within nlab latest changes the same way as I do the rest, the forum has a bit different formatting and makes it harder. Also nlab item jabberwocky has down there a link that it was mentioned with link in latest changes what I also find useful. I also do not find any argument in the saying that if I log to forum for looking at latest changes I will also see be “informed on the new things”. Thjis is not a feature but a DISTRACTION when I work hard and follow references and try to format my mathematical text. Forum is about policies and politics, and software.- Nlab is about mathematics. I like to havce that CLEANLY separated. The state of my mind is the prerequisite for working on nlab. The alternative is that I work only in my personal nlab if you impose this new policy of mixing with forum.
added something to directed space. Check!
added some $(n,r)$-topos cases to the “special cases” section at (n,r)-category
added a paragraph at About in the part starting with “If you find yourself annoyed by the state some entry is in…”. That paragraph is motivated by a recent reaction by somebody on some blog, who had indeed complained about some unfinished entry and after that needed some persuasion to help expand and improve it.
created stub for (infinity,1)-operad
added one and updated and commented another reference at Jacob Lurie
am proposing an expanded introduction and a supposedly suggestive slogan at (n,r)-category – check and see what you think
Zoran ?koda?: created Q-category (clearly unfinished; e.g. somebody could type the cosieve and Grothendieck topology-induced $Q^\circ$-categories and $Q$-categories of thickenings from Kontsevich-Rosenberg preprint as examples), wave, epipresheaf. New remark at formally smooth scheme. Updates to algebra, mathematicscontents and to the discussion at classical mechanics.
Urs Schreiber created entry for Constantin Teleman
David Corfield: created biology.
noticed that despite all the blog discussion, nobody has so far created field with one element…
created deRham space
created formally smooth scheme
Urs Schreiber expanded mathematicscontents and rearranged a bit – notably I added category theory, higher category theory, topos theory and higher topos theory (the lower case version!) which clearly all deserve to be there. I added some entries to go as sub-entries under higher topos theory mainly to balance that topos theory has its natural sub-entries there, but maybe debateable. Then I moved homotopy theory and its special case stable homotopy theory from the “Geometry” bit up to the “Structural Foundations” bit, as that seems to better capture it (anything that cares about things only up to homotopy is not geometry nor even really topology, but is higher category theory in disguise). By this logic, also rational homotopy theory belongs there, so I moved it up.
Urs Schreiber: worked on HomePage:
added the floating tables of contents for math, physics and philosophy. They are sitting there now to the left of the $n$Lab-contents. I am thinking that here on the HomePage this is a good thing. Besides the introductory text we keep there, we want to make sure that the reader’s attention is directed to tables of contents. I have heard of people who were pointed to the nLab, went to the HomePage for a minute and came back with the impression that there is nothing much to be found on the lab. While no table of contents can give an accurate impression of the full scope of the lab, the ideal would be that our main three top-level contents (math, physics, philosophy) will indicate the scope of topics and lure the reader further into the labyrinth. Optimally behind each of the links of the top-level toc the user finds another floating table of contents for the given sub-topic
I edited the bit about the forum. With Andrew getting ready to make “latest changes” be on the discussion forum, the old material saying that the forum is just for meta-discussion is outdated.
I included a link to the forum discussion on what the nLab’s scope is. As long as noone finds the time to wrap things up, this ongoing discussion is probably the best idea that we can offer as to what we think the nLab is or might be.
Jon Awbrey added articles or began content development at differential logic, differential propositional calculus, and universe of discourse.
Urs Schreiber: wrote a long bit at higher category theory. Rearranged some existing material in the process.
Jon Awbrey: Expanding on a note and responding to a query on the blog, I proposed several sources as “Precursors” to category theory. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain, but I might try to elaborate on it elsewhere … elsewhen.
Toby Bartels: Talk, talk, talk: SEAR, classical mechanics, category theory.
Mike Shulman: Motivated by recent discussions on the cafe, created SEAR, which has been kicking around in my head for quite some time.
Zoran ?koda?: created compact-open topology.
Zoran ?koda?: changes to A-infinity ring. I had to disagree at classical mechanics; created force. Minor changes to few other entries, like analysis, and to contents pages (geometry, mathematicscontents).
added a paragraph to enriched category theory (you can’t miss it, its the only genuine content there so far)
I am dreaming that eventually we’ll make the enties enriched category theory and especially higher category theory have content as nice as we now have at category theory. At time of this writing the entry higher category theory is a shame, given the nature of our project here. But I am growing fond of at least the first, stabilized part of category theory. It would be cool if we could do similar deeds at other entries of similarly fundamental nature
further expanded category theory - contents and added it as floating table of contents to more entries
(any volunteers for similar floating tables of contents such as topos theory - contents, enriched category theory - contents??)
Jon Awbrey added a subsection on categorical precursors to the References Section of category theory, but that’s already such a huge article that people may prefer to spin off a new page if it goes past a few links.
created category theory - contents and began adding it as a “floating” table of contents to some relevant entries.
following this blog discussion I added a paragraph “Terminology” to category theory
I also tried to incorporate the content of the query box that used to be in the paragraph on “Abstract Nonsense” by Zoran Skoda and Todd Trimble. I moved that discussion box to the bottom of the entry now. But if you think more discussion is needed, we’ll revive it.
Mike Shulman: Thanks Urs. I expanded 2-pullback a bit. Weirdly, the direct URL for weak pullback currently takes me to the old disambiguation page, which doesn’t seem to exist any more. Ordinary links like weak pullback are correctly redirected to weak limit however.
Lab Elf (financial department): weak pullback was still cached so a direct call got the cached page without a check to see if there was a corresponding page in the database. I’ve removed the cached page and it looks like it’s correct now.
added some links to the entry on Peter May
created stable homotopy theory - contents and added it as a “floating” table of contents to some relevant entries
rewrote A-infinity ring and E-infinity ring
created higher algebra - contents and added is as a “floating” table of contents to some relevant entries
created higher category theory - contents and added it as a “floating” table of contents to some relevant entries
moved to monoidal (infinity,1)-category material that had long been sitting at geometric infinity-function theory on operadic definitions of higher monoidal structures
Zoran Skoda alerts me that he has added corrections and caveats related to formal scheme and formal spectrum at A Survey of Elliptic Cohomology - formal groups and cohomology
reacted to Mike Shulman’s remarks at graph of a functor, cograph of a functor and at what used to be weak limit and is now renamed 2-limit by trying to implement the suggested changes. Mike should please have a look and check if it looks better now. I have to admit that I had forgotten that “weak limit” meant something else than 2-limit or other higher limits.
added the link to stable homotopy theory to the main Mathematics Contents
created coordinate-free spectrum and linked to it from spectrum (whose “Definition” section I slightly reorganized)
created symmetric monoidal smash product of spectra
added small paragraph pointing to this new entry to stable homotopy theory, smash product of spectra
created an entry inbound citations and linked to it from the main table of contents. Let me know what you think of this suggestion. See also the blog entry on it here.
Jon Awbrey added a link to a Forum discussion at relation theory.
Mike Shulman: Two questions at graph of a functor. One of them spills over into cograph of a functor and weak pullback.
Urs Schreiber slightly rephrased at formal spectrum: properly speaking that limit over rings gives the global sections of the structure sheaf, of course, not the structure sheaf itself
Jon Awbrey replies to a query at relation theory. Hey! that rhymes with “weak and weary”.
Zoran ?koda?: to support the development of entries on the basics of formal geometry created entry adic noetherian ring (I would like to warn Toby (who will likely like simpler generality) in advance that one needs to be very careful in treating adic situations without noetherianess, I do not feel competent to write without consulting literature such a more general entry). Thanks Urs for stimulating the expansion of the entries on the subject.
from more seminar notes filled in more material at
and started
many thanks to Zoran Skoda for fixing some nonsense that I committed in the “Idea” section at formal scheme
Jon Awbrey added some stuff about finite dimensional boolean coordinate systems to boolean-valued function.
Toby Bartels: A little more explanation of terminological variations at direct limit and inverse limit; also projective limit and inductive limit.
Jon Awbrey added an epigraph to relation theory. Exercise for the Reader: Show that every functional graph factors into an epigraph and a monograph.
added a reference to Peter May et al.‘s survey article to stable homotopy theory – also added a link back to stable homotopy category
filled in formal definition at elliptic curve, also that of the corresponding formal group law and some examples – but needs polishing/expanding
filled in content at formal spectrum
created Landweber exactness criterion
since I see entries pointing to “direct limit” and “inverse limit” I created entries direct limit and inverse limit. I know that we could just redirect to limit and colimit where the terminology is discussed, but maybe the reader following such a link will appreciated being quickly alerted to the terminological issue before being faced with a long entry on limits and colimits where this is hidden as a remark somewhere
slightly edited formal scheme: added an “Idea” sentence and highlighted the definition of formal spectrum a bit. In fact, created formal spectrum planning to have the definition there, but then hesitated. Maybe this needs someone more expert than me.
stub for structure sheaf
slightly edited the beginning of structured (infinity,1)-topos
created adjoint (∞,1)-functor
the essential information had before already been in the corresponding section at adjoint functor, to which I added the relevant link.
joined the discussion at graph of a function. I am thinking that this is best understood as a special case of a more general concept, for wich I created now entries
This has some nice applications. For instance one has that two functors $L : C \to D$ and $R : D \to C$ are adjoint precisely if they have the same cograph, up to reversal of arrows. Notice that, because the notion of cograph immediately generalizes to functors between higher categories, this is the basis for a definition of adjoint (infinity,1)-functor.
I have expanded the material at graph of a function accordingly. Also I made cograph of a function redirect to that.
Toby Bartels: Not done at graph of a function, Eric!
Jon Awbrey expunged an assortment of ephemeral animadversions at graph.
Eric: After some discussion with Toby, defined graph of a function as the category of elements of $F:\mathbf{2}\to Set$.
Jon Awbrey added at comment to the discussion section at relation theory.
Toby Bartels: Added diagonal morphism and two ways to look at it in $Set$: diagonal subset and diagonal function.
Jon Awbrey added a bibliography on relations and related subjects to relation theory.
Andrew Stacey there’s a discussion going on at the forum about designing a better system for recording these latest changes. If you have an opinion, please contribute! At the moment, it’s going on what Toby, Mike, and I think which may not be a representable sample.
Also, there was a brief glitch in the system that led to entities begin translated into their unicode counterparts (don’t worry if that doesn’t make sense). Unfortunately, this wasn’t compatible with iTeX and there may be a few ‘Unknown character’s lurking around. If you spot one, let me know and I’ll go catch it with my butterfly net. (It’s important to let me know rather than just correcting it yourself as it really messes up the diff
s so I need to fix it properly rather than just papering over the cracks.)
Zoran ?koda?: Urs seems to take derived algebraic geometry (see my answer/note there) as a higher algebraic stacks, and forgets deriving on the other side. Nonabelian cohomology results from right derived picture (quotients = colimits), and the missing part is to take the limits in derived sense, that is taking equalizers, intersections of subschemes etc. in derived sense as well. We should discuss that, replace the paragraph with the better one and after agreeing and explaining, erase the critical paragraph. In another paragraph the things are in place:
Where ordinary algebraic geometry uses schemes modeled on commutative rings, derived algebraic geometry uses structured (∞,1)-toposes modeled on E-∞ rings
Indeed, the higher stacks are about the (∞,1)-toposes, while the derived stacks ask also for the domain to be E-∞ rings. The “brave new algebraic geometry” on the other hand typically takes the second (alg geometry glued from spectra of infinity ring spectra), but not the first (higher stacks instead of schemes).
Mike Shulman: For those who aren’t reading at (n,k)-transformation, the proposal is to replace that unlovely term with Sjoerd Crans’ word k-transfor (so 0-transfor = functor, 1-transfor = transformation, 2-transfor = modification, etc.). Please comment!
Zoran ?koda?: stub derivator including few lines from triangulated category; maybe more discussion from there should be moved to derivator and just left a short notice at triangulated category on derivators (it seems in fact one wanted to talk about triangulated derivators!!), because t.cat. are a wide topic and the entry may expand in many different directions, while the motivation and the discussion may be useful at derivator. but have no time to decide and think of what is sensitive. Somebody should copy the axioms from Maltsionitis’ notes for derivator.
Jon Awbrey began watering his trans-plants at cactus language — bit by bit, you have to be very incre-mental with cacti — and started a parallel (tangential?) discussion at the $n$-forum.
Zoran ?koda?: additions to deformation theory, derived algebraic geometry; created cotangent complex.
Toby Bartels: I'm perfectly serious at (n,k)-transformation.
Todd Trimble: commented at lax natural transformation, and suggested a possible compromise at graph theory which I hope will be considered satisfying to all concerned. Thanks to Mike for creating icon.
Urs Schreiber slightly edited A Survey of Elliptic Cohomology - formal groups and cohomology and added plenty of links
Toby Bartels: More at graph and center, since there is no RSS feed.
Jon Awbrey is leaving the fray at The World According To Graph — which is clearly becoming more “productive” than “creative” — and suggests, as an interim measure, that he be allowed to store a few standard definitions at graph theory.
Mike Shulman: Replied at center and lax natural transformation, and created icon.
Toby Bartels: Thanks to David below! I have moved barycentric algebra to convex space after being more sure that this name is not already taken (but ‘convex set’ does conflict). Since the concept has been invented many times and has many names, let's use our own, which is a nice one. I forgot about the blog discussion before; I had a nagging feeling that this had come up once and I hadn't gotten around to commenting then, so I'm glad that David remembered.
Ryan Grady has given us A Survey of Elliptic Cohomology - formal groups and cohomology
Todd Trimble: Finally got around to replying to Mike Shulman over at lax natural transformation, with some responses of Ross Street and Steve Lack.
Urs Schreiber started adding to infinitesimal object a discussion for how one can understand Lawvere’s abstract definition intuitively as encoding infinitesimal extension. But am in a hurry and have to leave it unpolished for the moment.
Toby Bartels: Replies at barycentric algebra, evil, graph, boolean domain, center.
Jon Awbrey: Further discussion and some data at graph.
Mike Shulman: Expanded a bunch at center, and continued discussions at graph and evil.
Toby Bartels: More commentary at boolean domain and graph.
Todd Trimble: added still more to the long discussion at the bottom of graph.
Toby Bartels: Created barycentric algebra, mostly to explain the stuff about convex sets in the discussion at semicartesian monoidal category.
Urs Schreiber: motivated by Toby’s comment there I have now branched off the material at limits and colimits by example that describes a computer program to Paine on a Category Theory Demonstrations program. This is now linked to there from the section “Further resources”. I have moved the pertaining discussion boxes to the bottom of the entry.
Jon Awbrey: Piecewise discussion at boolean domain, but it will be later before I can get to the rest of the pieces.
Toby Bartels: Discussions at center, evil, graph, boolean domain, limits and colimits by example, semicartesian monoidal category.
Jon Awbrey: Continuing discussion at graph. I won’t try to note each entry here, unless that’s the rule.
Jon Awbrey: I added an Idea section to relation theory with what I can recall of how I got into that. Incidentally, the x-tended code for the amphora symbol (@) now causes Ruby to go off the Rails, so I had to use \text{@} instead.
Urs Schreiber: thanks, once more, to Todd, for the discussion of monadicity et al at limits and colimits by example. We should eventually brach that kind of discussion off into an entry in its own right and expand
Jon Awbrey entered the fray of discussion at graph.
Todd Trimble: Per Urs’s request below, I checked the limits in under-category he wrote, and added a remark at the end.
Zoran ?koda?: last night my battery bailed out when I was editing several entries so did not log what I have done. Now I do not recall all entries which I updated, except that I created deformation theory (so far only references and links), expanded derived algebraic geometry, added a reference to formal group and to quasicoherent sheaves. I thank lab elf for cograts for my entry 2000 which was however Grothendieck connection where I also made a small change last night (when saying $n$-costratification, $n$ refers to work with $n$-th infinitesimal neighborhood and not with $n$-categorical descent: the descent data were in Grothendieck 1-descent data). Today we have an excursion during the conference in Sevilla, so I will probably not be able to continue (have much to add to deformation theory etc.).
added a section on limits in under categories to limits and colimits by example and a detailed proof of how they are computed by limits in the underlying category – please check
added a linked table of contents at limits and colimits by example
added a query box at limits and colimits by example in the section titled “for programmers”. I am suggesting that since the material doesn’t actually use a computer program to explain limits and colimits but instead explains how to write such a computer program, the material should be moved elsewhere.
added an “Idea” section to n-localic (infinity,1)-topos
slightly expanded the remark under “Generalizations” at localic topos, trying to indicate the pattern
Urs Schreiber: re Toby’s remark below:
yes, true, the $(\infty,1)$-topos material is “Grothendieck-Rezk-Lurie $(\infty,1)$-toposes of $(\infty,1)$-sheaves”. If it weren’t so cumbersome to say this, one should make this explicit more often. But maybe we should highlight it at least more at beginning of entries.
Another thing I noticed that maybe requires more emphasis is that the $\infty$-stack-$(\infty,1)$-toposes that one gets from the standard models for infinity-stack (infinity,1)-toposes are far from being the generic case. Many Grothendieck-Rezk-Lurie $(\infty,1)$-toposes are not equivalent to these. (Compare Lurie’s discussion of topological localization, hypercompletion, n-localic (infinity,1)-toposes, etc.)
Toby Bartels: I moved free field (algebra) to free field on the grounds that (as with field itself) the algebraic mathematical meaning is likely to be our default here. But I might be wrong. In a similar vein, I suggested physical field at field.
Jon Awbrey made some attempt to reorganize the discussion at boolean domain. This is one of my main stepping stones, so I’ll need to keep the algæ at a minimum.
Jon Awbrey finished up the basic definitions and expository examples at sign relation.
Toby Bartels: I do enjoy it, Urs! But remember that, for Lurie, an ‘$\infty$-topos’ is not only an $(\infty,1)$-topos but in fact a Grothendieck $(\infty,1)$-topos. So when he says that a ‘$0$-topos’ is a locale, he similarly means that a Grothendieck $(0,1)$-topos is a locale. (An elementary $(0,1)$-topos is a Heyting algebra.) I also wrote (0,1)-category, since you linked it; that's a p(r)oset.
quick unformatted content filled in at n-localic (infinity,1)-topos, to be continued later, have to run now…
created stub for (0,1)-topos, linked to it from locale with a small comment – Toby might enjoy that – this mainly to remind me to extract the essentce from section 6.4.2 in HTT later. Will also create (n,1)-topos then
thanks to Todd for expanding at localic topos!
Toby Bartels: More at evil; we might actually be working out some mathematical facts here before too long!
Todd Trimble added some more to localic topos.
Jon Awbrey added a bit more content to sign relation and then broke for lunch. ($n$-tweet?)
created stubs for localic topos and n-localic (∞,1)-topos
added to Deligne-Mumford stack the alternative characterization as a 1-localic $G$-generalized scheme for $G$ the etale geometry (defined there). Also added a brief “Idea”-section
created affine scheme
created topic cluster floating table of contents (infinity,1)-topos - contents and included it in the linked entries
created object classifier and linked to it from (∞,1)-topos and Higher Topos Theory and subobject classifier
slightly reorganized and then expanded the topic cluster floating table of contents cohomology - contents. in that context I
created orientation, Spin structure, Fivebrane structure and slightly expanded String structure
briefly discussed/mentioned these in the examples section at quantum anomaly
and on that occasion created an entry for Ulrich Bunke whose recent article (yesterday!) I cite above, where he makes the old Killingback argument about how a String-structure makes the worldvolume anomaly of the heterotic string vanish rigorous
corrected the mistake at rational topological space that David Corfield spotted below
added to CW complex link to geometric realization
started rational topological space
Jon Awbrey added content to semiotic equivalence relation.
Jon Awbrey: Clarifying at graph theory and questying at evil.
Toby Bartels: Replies to Mike at evil and graph.
missed one train. Used the few minutes gained this way to quickly extract the following very brief entries from the notes mentioned below: multiplicative cohomology theory, even cohomology theory, periodic cohomology theory, Bott element – all these entries deserve to be greatly expanded, it particular by eyxamples, of course, but it should be a start
started turning some talk notes of a seminar into entries, but requires polishing:
the full raw material is at A Survey of Elliptic Cohomology - cohomology theories. Using this I have so far split off cohomology theory, Lazard ring, complex cobordism cohomology theory and reduced cohomology
wrote a somewhat revisionist “Idea” section at Grothendieck connection. Notice that it is in particular the Breen-Messing reference cited and discussed at infinitesimal singular simplicial complex that allows me to do that! (meaning: I am not making this up, but just putting the pieces together)
Jon Awbrey added a page on graph theory. The page on graph has become too baroque to fix, but there needs to be a place to record the basic definitions of graph theory that are actually used by the larger schools of math folks who actually dare to call themselves graph theorists. This is stuff that is more in the back of my mind than the forefront of my attention, so I’ll add to it over time as other work recurs to it.
Rafael Borowiecki: Replied Todd Trimbles question at Timeline of category theory and related mathematics.
Urs Schreiber started keyword-list entry Structured Spaces and in that context also started generalized scheme
Lab Elf (numerological department): Just thought I’d congratulate Zoran on creating the 2000th page on the nLab. According to the database, it was smooth morphism of schemes. For those who prefer other coincidences, skewfield was our 2009th. Of course, in this more modern age we ought to really celebrate coherent sheaf instead. Whichever we celebrated, it would be Zoran that would get the metaphorical bottle of champagne as he created the lot.
changed the coding of the floating table of contents cohomology - contents according to the recent discussion on the forum and added a few recent entries to it
slightly expanded integral cohomology
added a web reference by Nora Ganter (created stub fo that) on topological modular forms (created stub for that) kindly pointed out by David Roberts to A Survey of Elliptic Cohomology and to tmf
it seems that yesterday I also created stable homotopy theory
Jon Awbrey added an epigraph to evil.
Todd Trimble: responded to something Rafael wrote at category theory, and asked a question at the bottom of the timeline page.
created derived algebraic geometry
wrote a bit of summary at A Survey of Elliptic Cohomology
started elliptic cohomology
so far with quick stubs for line bundle, cohomology ring
expanded the content at Jacob Lurie, fixed the links and added A Survey of Elliptic Cohomology
merged the former material at ∞-topos with that at higher topos theory and expanded and slightly rearranged the latter.
coded the “floating tables of contents” for the topic clusters at mathematics and rational homotopy theory according to Andrew Stacey’s suggestion on the nForum – see here
Replied at category theory.
Wrote a little more on extended topological quantum field theory but don’t know the right references. Put that request in a query box.
Debate at the timeline.
Note spelling: Saunders Mac Lane.
Zoran ?koda? inserted and reminded of work of Rezk and Toën-Vezzosi on higher topos theory preceding the marvelous Lurie's work.
Andrew Stacey: without wishing to join in the fascinating debate as to whether the timeline should be kept in sync with Wikipedia, I’d just like to expand on my comment about asking the question on the forum. The specific question on timeline is technical in nature (“how do I deal with 1500 links?”) and therefore most likely to be answered by one of the more technically minded people here. Some of those people do check every page on the lab for every revision, but others don’t. However, they do check this page and they tend to check the forum as well. The best way to get your question seen is to put a brief note here and link it to a discussion on the forum. Also, the more detailed and precise you can make your question, the easier it is to understand and to answer and therefore the more likely it is to get an answer.
created a stub entry for Samuel Eilenberg and put hyperlinks under the names of Eilenberg and MacLane at category theory.
expanded at infinity-stack the first paragraph of the “Definition” section and added a link to sheaf of n-types.
created sheaf of n-types which was requested in the “Timeline” entry. But I made this essentially just a commented redirect to ∞-stack, because it’s just another word for that.
expanded the introduction of AKSZ theory a little, added the original reference and linked Kontsevich’s name there to the new entry on Maxim Kontsevich and added a paragraph that tries to briefly put this in context with related existing nLab entries. But the entry is still missing a discussion of its subject itself. I have some old blog material on this, but this deserves more spare time than I have at the moment.
added links back and forth between the new higher topos theory and the old ∞-topos. Probably some reorganization of the material over these two entries would eventually be reasonable.
added plenty of hyperlinks to the entry on Maxim Kontsevich – many of them point to existing nLab entries, many others point to nLab entries still to be created (and lots of them would be highly desireable)
Toby Bartels: Created a stub higher topos theory (not to be confused with Higher Topos Theory).
Benoit Jubin: asked a question at monoidal category about the necessity of requiring $\lambda_1=\rho_1$.
Tim Porter: On the issue of stacks, Deligne and Mumford explicitly (p. 97 of their famous paper) use the term ‘stack’ as an English translation of ‘Champ’ and attribute that to Giraud in Cohomologie non-abelienne. This latter source was published later than Deligne and Mumford’s paper but is refered to by them as ‘University of Columbia’. Giraud was a student of Grothendieck.
Zoran ?koda?: surely Grothendieck invented stacks in general categorical sense and had a picture in various setups; Deligne and Mumford did invent a particular kind of algebraic stack and tailored it toward a very specific application.
I was before talking about edit 143 of the timeline by Toby Bartels. I am now trying to figure out what it changed. The other edits i understand.
Added a query box at Timeline of category theory and related mathematics to hear what others think about the first entry in the timeline regarding Cayleys paper.
I must correct you Zoran at a point. I never said the entry must look good but i want the timeline to look good. This means links, easy to read, no stuff that should not be there and it should of course be correct. Those who know the years,names and category theory would see if it was not correct and say it looks bad.
Since we are on the subject history. I Credited Deligne-Mumford for inventing stacks. But i recall rumours that it was Grothendieck that invented stacks, without any references.
Zoran ?koda?: added redirects and a reference to quasicoherent sheaf; expanded representation theory; created EGA (just an introduction to the entry, links and toc missing); created orbit wanted by coadjoint orbit; more importantly for the present needs, wrote Grothendieck connection (entry 2000 :)), required both by the timeline and by the current interests of the project pushed by Urs which I try to help and discuss; and it also refers to some things I was many time mentioning (and even to some ideas behind my preprint on cyclic comonads and related papers by Menini-Stefan and Böhm-Stefan). Wrote Poisson manifold and coadjoint orbit (unfinished). No, Rafael, I was not trying to find oldest instance of category theory. But Hilbert’s first entry and also things about Whitehead etc. nonabelian invariants require the earlier appearances of such ideas if they existed. Look, the main theorem of Cayley in modern language says that the resultant of polynomials is a determinant of certain Koszul complex. As far as Galois, I think it should absolutely be in timeline, definitely, not only because of the notion of the group, but in fact Galois theory itself is in a spirit and a stimulus of much of the modern category theory – torsors, Grothendieck Galois theory, equivariant descent, Galois descent, Joyal-Tierney, Hopf-Galois to mention a few (On the other hand, the notion of an abelian group is essentially in Gauss’ Disquisitiones Arithmeticae in pretty clean form, according to my friends who read it carefully; I can not judge). The Klein’s Erlangen program is a related ideological item, but more disputable. I still do not understand what do you mean by that moving again the wikipedia and overwriting $n$lab version depends on ability to do links. If you change links to wikipedia somehow automatically to the format which finds the true wikipedia pages this will be good for most of the items, but wrong for those few items where we already do have nlab entries. So it is a problem of selection.
Rafael Borowiecki: When i was writing i once by accident updated the timeline at wikipedia and undid the change. If you look at it from the history you will see that i have corrected some of what you wrote and i will with interest look at the rest. I find the dates usually on internet which mean they could be wrong. I did not include Poincares Analysis situs for progress on group theory but topology which is one of the related themes of the timeline. As for Cayleys paper i would like to hear what others think. But it looks to me you tried to find the earliest possible instance of category theory. Then Galois theory is earlier. I think of it of course as a precursor to modern Galois theory but did not include it.
Toby Bartels: I have some opinions on the Timeline of category theory and related mathematics, which I will put there where they belong.
Zoran Skoda: created an entry on Maxim Kontsevich as his name is quoted in timeline and some other places in nlab.
Zoran Skoda: The same way one could say that Poincare’s papers done nothing on group theory. He does many things about groups completely in the language of manifolds, but in fact he proves the theorems on fundamental group, and these were transferred to group theory later. The homological algebra of Hilbert is equally linear algebra as is homological algebra of Cayley. Cohomologies in different language were used extensively by early Italian school of algebraic geometry; ask Japanese algebraic geometer Mukai to explain the 1899 paper (I think) of Castelnuovo with Castelnuovo’s arguments literally, just with modern names for the quantities (it is all about cohomologies). I do not know why do you care that the entry LOOKS GOOD. I think it would be more important to be CORRECT, I listed once several instances of suspicious dates, and nobody cares about what is more important than syncing. To add new ones it is NOT true that localization is a special case of descent as it says in 1960 entry on descent within wikipedia timeline version; surely localization and descent can be combined in very nice ways, or sometimes phrased in the same language but the descent is descent and the localization is localization. Well descent data and the localized category can be both made comodules or modules over some comonad or a monad but this is a different issue and neither is special case of another. Rosenberg’s proof of the reconstruction of scheme is not written first time in the 1998 paperon nc schemes, that paper has just appendix with a SKETCH of the proof which is in its full version in his earlier 1996 Max Planck Bonn preprint (pdf), some form of which is published in another journal also in 1998, with submission January 1997; in any case it is a different paper than noncommutative scheme paper. Similarly, 1960 date for Grothendieck’s formal schemes is wrong, as the Bourbaki seminar paper for 1958/1959 is having a full article with already deep results (like Grothendieck existence theorem) on the subject. Look bibliography to formal scheme. 1960 for descent theory may also be too late though I am not sure at the moment, I am almost sure that one of the parts of FGA for descent has been published before 1960; just look for FGA (probably in Vistoli’s survey you can find the year for the reference). For triangulated categories one should list (unlike wikipedia version of timeline) not only Verdier but also Grothendieck who was the true discoverer (and gave the list of chapters and main theorems to Verdier to prove and write up,a s he was usually doing with his students). You see these complaints I wrote only after 2 minutes of looking superficially at several lines of timeline. The timeline needs tens of such corrections historically and not the syncing,colors and look.
Rafael Borowiecki: Zoran, the migration will ultimately depend on if i am able to do the linking. I could completely not care about the nLab timeline but i want it to look good. The long entries will be as short/long as they are now. I will try not to loose anything and discuss the entries i would remove. AST alteady exist as do pages for the other long entries. Regarding Cayley i have seen the paper long before and have it on my computer. Cayley calculates invariant theory in coordinates. The paper do not define any categorical concept or prove a categorical theorem. Nor do it introduce any method used later in category theory, it is just polynomial algebra. I would say it don’t start homological algebra. You could put it as that it anticipated homological algebra but i don’t think Cayley thought about this paper that abstractly.
Zoran ?koda?: Rafael, when you opened timeline in nlab you did NOT tell us, the conditions/plan of syncing, which is fundamentally incompatible with nlab and wikipedia as each of them has limitations AND advantages. For example, we like book entries in nlab; timeline has some entries in the tabel very short, some hugely long: e.g. the wikipedia has huge entry of about alf a page on a book of Joyal and Moerdijk on algebraic sets. Why not have a separate entry in nlab for that book with all the material and in nlab entry for that book just say book algebraic sets, yeas and that’s it. Second new migration would take tens of hours of time to make links compatible with entries in nlab, some of which can not be automatic. How Cayley’s paper benefited category theory ? Jee, you have tens of etries on homological algebra; including the Hilbert’s which are about the SAME stuff, just much later. How do you expect a collaboration on an entry if you are going to just decide out of your taste what is important ? Even if we talk about papers which wree anticipating developments in other works by over half a century ? You are concerned about syncing and difficulties. There is a wikipedia and there is nlab. When it is easy to borrow and coopearte why not. When it is difficult and creates problem just the heck with it, let’s develop aturally two versions. No sync…
Rafael Borowiecki: Replied at the timeline of category theory. Zoran, my original plan was to have the timelines synced to optimize both timelines and i will try to do so. I will also try to have good links. Right now the wikipedia timeline contains almost all entries and information in the nLab timeline and very much more. So at the moment it would be nLab that benefits most. I will look into your changes once again and try to keep them. It is easier to only copy the links than to find them. You have not seen the new version but, as for Cayley i just don’t see how his calculation benefited category theory so i removed it, but this is a discussion for the timeline page. I also recall removing the deRham theorem since it don’t really fit with the structure of the timeline. I have not included dualities. But this one i can change back since it was a very important discovery about cohomology and there are no rules to follow any structure. I will check more now. Then i wish people added so much to the timelines it would be impractical to sync them. Now that nLab is fast enough it should go much better to edit the links.
Zoran ?koda?: created internal relation. I was once working on replacing tens (and spend hours on this) of wikipedia links in timeline with our own links, and even created new entries in nlab to support the new links in nlab. For example I created the entry for Otto Schreier in nlab to support the quotation for Schreier in nlab version of Timeline. I also do not understand why things like the Cayley 1843 entry are ignored (and hence will disappear in new migration); I spent hours of time looking into references which I recalled vaguely to confirm what I thought about it. I see no reason for wikipedia to overwrite our work on changes. 80 links changed in single day is possible done by me; I recall that I did work once on making many links either more functional (including making the blind link to wikipedia link) or update them with new biography entries in nlab. I would not say that in that particular day only the links changed.
Jon Awbrey made a first pass at formatting Trimble on ETCS III and thinks to have earned himself a nice Labor Day vacation, so if it’s messed up don’t tell him till Tuesday.
Rafael Borowiecki: Urs, i have taken care of that. I first updated the wikipedia timeline to match the nLab timeline. But a discussion might be at place since i have removed some of Zoran Škoda’s entries. I was not able to see and do one change thought, there is one revision that changes something in most of the 80 first entries or so. Maybe only links. I only took a quick look, and i am now thinking about the link problem. I found nLabs way of comparing revisions often very hard to read. I think it colors much more than need to be.
Zoran ?koda?: oops, the link to Cartan Seminar at numdam was one char too long at Timeline; sorry. Regarding that the nlab has both different rules, format, link capacity, side resources etc. than wikipedia, that after so many updates are done in nlab version on our side, it woudl make no sense tooverwrite the nlab version of timeline with a new migration of wikipedia. One can update some particular items, but migrating it as a whole would mean relinking the part which is already relinked in nlab version. So, once the original bulk of timeline has once being moved the two timeline entries may live their separate lives and occasionally some individual additions or links could be manually added to borrow from nlab to wiki or other way around, by the criteria and will of nlab contributors while copying news to nlab and wikipedia contributors while copying news to wikipedia. It is too late to do bulk migration again; and wikipedia while better in some items, the nlab is better in some other additions to timeline which never made into wikipedia. Or I misunderstood something. I see no purpose into maintaining the two versions mutually equivalent; who wants to see another version can do this by clicking. The cooperation is rather to start the bulk and then to grow any way it likes.
Urs Schreiber – question to Rafael Borowiecki: below you write
The same timeline at wikipedia has/will have soon about 1500 links. When i migrate it to nLab again, and better than the last time, i need to change the links
What do you mean by “migrate”? The nLab version of the timeline has now many entries and edits that don’t seem to be reflected in the Wikipedia version. No?
Rafael Borowiecki: Replied to Zoran’s question.
Zoran ?koda?: put a query into the Timeline entry: at numdam one can find the Cartan Sem from 1948, but I can not find there the write up of sheaf theory those some related notions in non-sheaf language can be easily found. Am I blind ? numdam 1948 Cartan Sem. Timeline claims 1948 WRITE-UP. So where it is ?
slightly expanded Lie algebroid and added several links to entries that didn’t exist back when this was created but do exist now
in this context I made Atiyah Lie algebroid redirect to Atiyah Lie groupoid
created tangent Lie algebroid
The Timeline of category theory and related mathematics is repaired thanks to Andrew Stacey. See the new question there about updating links in a new migration.
Andrew, i am glad that you are interested in my big problem. But i don’t really understand your question. Is it not enough to ask the question at the timeline page and say here that i have added a problem to solve to the page? Perhaps the question at the timeline was not clear. The same timeline at wikipedia has/will have soon about 1500 links. When i migrate it to nLab again, and better than the last time, i need to change the links to link to correct pages at nLab. It is only some of the names that need to be changed to link to correct nLabs pages, which often have different names than those in wikipedia.
Zoran ?koda?: created fibration of points following Borceux-Bourn.
Andrew Stacey: I have implemented all the little database tweaks that were needed and done my best to reverse all the truncations. Please see this comment for details. Please also check if a long page is how it ought to be (thinking particularly of the timeline).
The main thing to note is that although the limits are larger and are sufficient to accommodate all that was on the old lab, there are still limits. In particular, page names and redirects are limited to 100 characters. Page contents is a little bigger!
Talking of the timeline, incidentally, now that I can see Rafael’s question, could I ask him to ask the question again over on the Forum with at the very least a link to where I can see what it is that needs to be converted? Thanks.
Zoran ?koda?: additions to Ieke Moerdijk
Tim Porter: I have removed the blue boxes as suggetsed by Urs (see below).
Zoran ?koda?: created the entry for the monograph Borceux-Bourn and extracted some material to add into Mal'cev category. Created Mal'cev variety including the definitions and redirects for Mal'cev operation and Mal'cev theory.
created entries for Saunders MacLane, Gonzalo Reyes and Ieke Moerdijk and included links to them where we cite these people as authors (but I will have missed many pages where we do)
am asking for discussion of my latest formatting decision concerning these floating tables of contents here on the forum
expanded the entry dg-algebra, moved the discussion there to the bottom, as I think it has been addressed (but Toby, let me know if not)
I find it kind of a pity that this entry exists in parallel with differential graded algebra. I understand that the motivation was that one entry gives the detailed component description while the other gives the abstract nonsense definition (monoid in chain complexes). But this is a general effect in the nLab and we should keep such things in different subsections on the same page. Maybe let me know what you think
added floating table of contents to the “lexicon” entries on differential graded structures that Tim Porter created a while ago. See for instance starting at graded vector space.
(these tables overlap with Tim’s blue alert boxes. I am thinking we could remove these boxes now and let the table of comntents server their purpose, but before i do this I want to hear what Tim thinks about. I’ll contact him)
Jon Awbrey made a first pass at formatting Trimble on ETCS II, but it will need to be checked.
Todd Trimble: wrote article on tree.
Zoran ?koda?: created formal group scheme also far from finished. Maybe John would like to explain connections to the Witt ring ?
Rafael Borowiecki: Wrote a hopefully not too long answer to the long discussion at category theory.
Zoran ?koda?: created formal scheme but it is far from finished; small changes to few related items (e.g. Kähler differential).
Benoit Jubin has kindly corrected some fonts at monoidal category. Welcome, Benoît!
Toby Bartels: Answered the open question at An Exercise in Kantization.
Jon Awbrey added a stub-link at semiotic equivalence relation — and I see by the clock on the TARDIS Wall that the Synchronoplastic Infundibulum has hic$\cup\partial$.
Zoran ?koda?: added some references to supermanifold. I agree with Urs that the co-things when the entries contain predominantly the definitions and non-specific information should be just under the things. However often the cothings are very unlike things in practice. For example, homology and cohomology in abelian categories is just the same and dual; however in geometry homology and cohomology of spaces are rather different; for example there are finiteness conditions in homology which are absent in cohomology. Naively defined Čech cohomology is a cohomology theory and Čech homology is not, as it fails exactness…but the coherent repair works. Or the rings. Artinian and noetherian are dual conditions, but for unital rings the unit breaks the symmetry, hence every unital artinian ring is noetherian but not by far other way around.
Lab Elf (Swiss department): I think I’ve fixed the timezone. I guess the real test is when I submit this page. Let’s see now, it’s about 12:50 UTC, so click ‘Submit’ and … 12:51 is the reported time. Yippee!
Andrew Stacey: The memory upgrade has happened. Our IP address has changed so if you can’t access the nLab then you need to … err …
Urs Schreiber made the following keywords all redirect to fibration sequence: cofibration sequence, homotopy fiber, homotopy cofiber
(this is supposed to be in line with what I think is a general strategy we should stick to: that all co-things are discussed in the same entry with things, since otherwise we get huge and unreasonable duplication)
Zoran ?koda?: created free field (algebra), perfect field, algebraic group.
Lab Elf (children's department): We’re getting a memory upgrade sometime soon. This will involve a downtime of approximately 35-40 minutes (they have to shift our “slice” to another machine to accommodate the upgrade). I don’t know yet exactly when this will occur and I may not get notice in time to post it here (I’ve requested that it be ASAP). For obvious reasons, if I do get notice of when it will be then I’ll put an announcement on the Forum and somewhere appropriate on the Cafe (I guess the ‘nLab migration’ thread seems most suitable).
Urs Schreiber: expanded generalized (Eilenberg-Steenrod) cohomology
Toby Bartels: In answer to Jon Awbrey's question,
What day is it? it's still September 2 UTC, but for some reason the Lab is now on UTC+4, which makes it September 3. Hopefully we can get it back to UTC, which is the standard for international sites; but if not, then I'll probably just edit the ‘UTC’ up above to ‘UTC+4’ and leave it at that.
Lab Elf (Swiss department): On the TODO list … Actually, maybe the TODO list ought to be a little more explicit. I’ll stick it on the forum.
Jon Awbrey finished formatting triadic relation.
Urs Schreiber tried to usefully rearrange the table of contents at HowTo into subsections a bit, just a suggestion, probably not optimal yet, but I felt the reader might wish to have an easier overview
Toby Bartels: Made a table of contents for HowTo.
Mike Shulman: A bit more on displaying MathML at HowTo.
expanded the beginning of extended topological quantum field theory, also added further links to existing entries
further expanded equivariant cohomology a bit: made the essential idea a standout box and added group cohomology and local systems as examples.
Replied at Bousfield localization.
Replied and did some minor changes on extended topological quantum field theory. I am waiting for the experts to improve what i have written before i write more.
As for the timeline i am glad that it can be fixed but how about the long titles? Ah. the nForum.
started an entry on equivariant cohomology
I agree with Andrew: single long pages are not so good for the reader. An entry that becomes very long should be split into an overview page with a linked table of contents and sub-pages. We did this for instance for gerbe.
added to HomePage and to HowTo a note on software prerequisites for displaying MathML. At HowTo this discussion should eventually be expanded.
I changed links throughout the Lab to the pages Chevalley-eilenberg algebra in synthetic differential geometry and to Verity on descent for strict omega-groupoid valued presheaves to the new truncated title names, so that they will still work. There are more entries for which this is necessary. See the discussion at the forum.
Andrew Stacey I’ve written enough on the Instiki/MediaWiki issues elsewhere and I’m not going to rehash them here (or even link to them). In short: it ain’t gonna happen. The issues we’re having is purely a matter of database differences - it’s nothing to do with Instiki itself. I doubt many people do a database migration - certainly none of the nonsense (abstract or otherwise) that I’ve read has mentioned the problems we’ve had - so the issues aren’t well known. I’m finding them out as we go along. I apologise that it’s a live test, but there were only three serious beta testers and they didn’t pick up on all of these issues as there were only three of them.
I don’t know why splitting the timeline up wouldn’t feel like 2009. I think that long pages are a hangover from the old days. We should have shorter pages included in to bigger pages (which, incidentally, is what MediaWiki does only it does it without telling you). “Pages” should be layered so that a visitor gets a broad overview first, then clicks through to get finer and finer details. One long page seems to miss the point of hyperlinks.
However, as has been pointed out in elsewhere, this is a lousy place to have a discussion. These are interesting points to discuss, but distracting on this page, so if anyone would like to pursue them further, I suggest we shift it over to the forum.
What is more important is to let me know (preferably on the forum) of any other issues with the migrated site. Now that my eyes have uncrossed, I’ve realised that I was misreading the MySQL article on storage limits and we can have superlong pages so we will. Soon. I promise.
(I still say it’s a bad idea)
Did some editing of center (added categorifications) and normalizer, and created centralizer.
Tried to remove some of the duplication from dualizable object, compact closed category, and rigid monoidal category, but some is still left. Perhaps the latter two should really be combined on one page?
added links back and forth between the new extended topological quantum field theory and the old FQFT – notice that there is a bit of overlap, we may want to rearrange material eventually over these two entries.
replied at category theory (down in the query box at the bottom)
Jon Awbrey added a stub and a few links on the subject of inquiry.
Rafael Borowiecki: Wrote the beginning of the well deserved page extended topological quantum field theory.
Rafael Borowiecki: Just as an interesting fact the new timeline which is not finished is 113kb, then extract the 4 or so long entries that were moved to separate pages and add literature, references and the long discussions. So how are other sites doing it? It looks like it is just nLab that runs into different troubels (even before the migration). I could mention more such as line breaks that is not working smooth or at all, but not now. I can not compare it to many sites but one is wikipedia. Even for editing as Zoran Škoda mentioned, wikipedia has no problem in editing parts of a page. I don’t know which technology nLab is using (except a part of it is called instiki) but how about an upgrade to such technology as wikipedia is using? In fact everything that i noticed don’t work here work in wikipedia. In all, the timeline could be split in two year parts and one main page with discussions, but i don’t really like it. Then it would not feel like 2009.
Zoran ?koda?: Thanks, Andrew a lot for all you are doing. Good night! I am loggin here another concern about terminology abstract nonsense. I am moving much in (predominantly noncommutative and algebraic) geometric community and my exprience is that when somebody says they proved a fact by abstract nonsense it is NOT confined to categorical methods only but to any CLEAN and GENERAL methods “from the book” as opposed to specific unclean improvizations tailored to a very specific circumstance in question.
Andrew Stacey: My eyes are beginning to cross when reading the MySQL manual. I may have been misreading a couple of things to do with data storage and it may be possible to get around the timeline problem. However, I still think that long pages could be better split up.
I sincerely hope that the lab survives the night, but I’m going offline now so please be patient with it!
Zoran ?koda?: of course, this is not a solution to the database problem, but I anyway think the discussion part could be separated from the main table of Timeline and the Timeline could have a separate part till 1960 say, then 1960 till 1989 and then third since 1990 (for example, better estimates possible). That would be easier for editing, with big file it is difficult to scroll when editing anyway. I created normalizer, center (with a word on and redirect centralizer) and holomorph. Please check, it is elementary, but it was a quick writing.
Andrew Stacey is seriously considering finding The Doctor and borrowing the Tardis to go back and have a Serious Word with the designers of sqlite3. (Anyone who gets the reference, I have a great photograph of a bus seen here in Trondheim that proves that The Doctor’s greatest enemies are sneakily planning their next invasion from Norway. But I digress.) The problem with the timeline is the same as that with the long page names (and with an old problem in the testing stage with stylesheets). It’s down to a fundamental difference in design between sqlite3 (the old, slow database backend) and mysql (the newer, snappier model). Basically, while both allow you to declare certain entries to be a certain type, sqlite3 then proceeds to ignore that type. Mysql (and just about every other database) enforces it. So when Instiki says “page names should be at most 60 chars long”, Mysql truncates them to 60 chars while sqlite3 merrily accepts page names as long as Lanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch and back again. Twice. Similarly, where MySQL has a limit on lengths of rows in its database (happens to be 65535 bytes), sqlite3 merrily goes on accepting data as long as it gets it.
You can see where this is going, can’t you. Yup, timeline hit that latter limit. It’s currently over 80000 characters, and some of those are unicode so I’ve no idea how many actual bytes it is!
Before anyone suggests going back to sqlite3, let me point out that we can’t scale up with sqlite3. So that’s a non-starter. There are complicated possibilities in which we have more than one row for a page, but the absolute simplest would be to split long pages into smaller ones and then include them from the main one. So we could split the timeline into, say, decades and then an extra bit for the discussion and simply include them all on the main timeline page. That would also make editing the page a bit slicker and quicker.
If that is acceptable, then I can load up the timeline in two segments for someone to carve up into more sensible pieces. It’ll be tomorrow now before I get round to doing this (sorry).
I’ll also have to figure out whether any more pages are affected by this. I’m afraid that I’ll have to roll these back to how they were when the lab was migrated (but presumably no-one’s actually tried to edit one of these truncated pages, otherwise there’d’ve been more bugs noted here).
Todd Trimble added a teeny bit to locally convex topological vector space. I hope to be more in nLab editor mode soon. Congratulations on a successful migration (with big thanks to Andrew Stacey).
Andrew Stacey: I’d hold off on the champagne for a little bit …
Zoran ?koda?: query in category theory: I think that blaming the terminology abstract nonsense to predominantly non-likers is misleading and that the wikipedia is this time more correct than nlab.
Jon Awbrey: I have always understood the term “abstract nonsense” as a pun on the sense of the word “sense” that means “direction” — hence “abstract nonsense” suggests something like the “formal path-independence” of commutative diagrams. I’m sure I mentioned this to several people back in the day, and they all said something like, “well, duh.”
Zoran ?koda?: I never heard of such interpretation; plus this interpretation would not survive in other languages like Russian and French where the direction and sense/nonsense do not mix like that. Russian version of abstract nonsense is абстрактная чепуха.
Jon Awbrey added stubs and links at sign relation and triadic relation.
Urs Schreiber: replied in the discussion at the bottom of category theory – and have a question
Urs Schreiber WATCH OUT WITH LONG ENTRY NAMES – see the $n$forum discussion. Some long entry names got truncated in the migration. the entry “Chevalley-eilenberg algebra in synthetic differential geometry” for instance is now called Chevalley-Eilenberg algebra in synthetic differential geomet
See “all pages” to find out the truncated entry name of an entry that you know should be there but is missing.
Rafael Borowiecki: To Andrew Stacey. The whole bottom part of the page Timeline of category theory and related mathematics is abruptly missing. Which is a lot, not only my question. Since i have the full version loaded in a browser i could try to reconstruct it but i would prefer if you did a rollback if you can.
Jon Awbrey added content to hypostatic abstraction.
answered Rafael’s plea for a definition of ‘CW complex’ in that big discussion on category theory, and also commented on Urs’ remark about ‘simplicial complexes’;
completed the definition of monoidal category by adding the triangle equation;
added some remarks on right vs. left duals on rigid monoidal category;
noted that the $n$Lab crashed a couple of times while I was doing this. Unfortunately I did not get a screenshot of the fancy error message.
Andrew Stacey: Yes, we hit our memory ceiling a couple of times. I’ve lowered a couple of settings to try to ensure that we don’t do this again but it’s a bit experimental as to what the best settings are. It’s all a bit of a learning experience for me! (Perhaps I shouldn’t admit to that …)
Zoran ?koda?: I restarted the system and now IE renders normal subgroup correctly. This is strange as it had problems only with new entries normal subgroup and normal closure (even after many reloads) and rendered correctly the other entries. Now after reboot even they appear correct.
Andrew Stacey: Okay, sounds like it was a cache bug. During the changeover, various addresses pointed all over the shop and there are redirects going all ways from Sunday, so it’s not surprising that a browser get confused. Clearing caches is probably a good idea. It will take a while before ncatlab.org properly points here for everyone (for example, from my work machine it was working from about midday; now at home then it still resolves to the old lab). But if you type ‘ncatlab.org’ into a browser you will always end up here, it just might be via a slightly circuitous route.
Zoran ?koda?: I just created normal subgroup, normal closure, but they do not render correctly on my IE. Is this a new-system glitch? The letters and formulas are one across another. Did not make last night logging that I added a paragraph or so on the Jacobi matrix and the application (Alexander polynomial) into the Fox derivative. I also created derived affine scheme in the sense of Toen et al.
Andrew Stacey: No idea! Can you send me a screen shot? Unfortunately, the Windows machine that I have control over can’t connect to the wireless network here (Oh, the irony!) and the windows machine that I don’t have control over doesn’t have MathML support.
Andrew Stacey: The migrating eagle has landed.
There will inevitably be hiccoughs, hangups, and hassles. Please log them over at the nForum. Also, if you notice weird behaviour then there may be an explanation of it over there (just because I know what causes it doesn’t mean I’ve implemented the fix yet).
Posed a question at Timeline of category theory and related mathematics regarding a new migration: How do i handle to update most of 1500 links!?
Suggested that manifold objects should be treated or at least mentioned at manifold.
Provided references for my question at Bousfield localization.
Split the subsection what is category theory at category theory into two parts: In the narrow sense and In the wide sense. This makes sense.
Added briefly how toposes and higher categories come into category theory as a foundations at category theory.
Added what it means for category theory to be a unifying tool and language in mathematics at category theory.
Replied to the discussion at category theory.
I see the migration went well, at least so far. :)
(Andrew Stacey: actually, it happened after you posted this, but thanks all the same!
Toby Bartels: Happy September!!!
Toby Bartels: Now, you know it's not September for another half hour, right? (^_^)
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Last revised on August 23, 2015 at 22:25:35. See the history of this page for a list of all contributions to it.