# nLab 2009 September changes

##Archive## * [current](http://www.math.ntnu.no/~stacey/Mathforge/nForum/?CategoryID=5) * 2009 September * 2009 August * 2009 July * 2009 June * 2009 May * 2009 April * 2009 March * 2009 February * 2009 January * 2008

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 The announcement of the change to the Forum and the reasons for it have been archived.

## 2009-09-30

• Toby Bartels: The lab elves are going to try to convince people to use the Forum for latest changes in October; see the new section about this at the top of the page. (If the instructions there are unclear, you can edit them now; I will move the final version to a permanent post on the Forum in 23 hours, after which you won't be able to edit them.)

## 2009-09-27

• Mike Shulman: In response to the discussion at choice operator, I started SEAR+ε 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.

## 2009-09-22

• 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?

• 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 Škoda expanded proper map.

• Urs Schreiber

• 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 Škoda 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:

* tic (any old list item will do the trick here)
{:toc}
• Urs Schreiber

• 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…

## 2009-09-21

• Heated discussion at SEAR.

• $\mathbf{Cat}$ fight?
• Jon Awbrey is setting some tables at differential logic.

• 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.

## 2009-09-17

• 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.

• 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.

## 2009-09-16

• 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

• That sort of thing doesn't give me any idea about what an $(n,r)$-category is … although it does tell me what an $r$-directed $n$-type is! It's important, good stuff, but I wouldn't put it in the lede. —Toby
• Zoran Škoda: 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.

• 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.

• David Corfield: Seeing “comparative $\infty$-categoriology” there, does anyone have thoughts on Borisov’s work? Perhaps we need to wait for the sequel.
• 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.

• Jon Awbrey: A bit too close to SOAR. But if you put your terms in alphabetical order you’d have ERAS, which would also be mnemonic for the fact that elementhood is a relation. Hm³, is there such a thing as mnepic?
• Zoran Škoda: created compact-open topology.

## 2009-09-14

• 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 Škoda: 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.

• 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

• 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

• Turned set into an essay (Was sind und was sollen die Mengen?) on the issues involved, particularly trying to keep them (foundational style, smallness, skeletality) separate.
• Thanks, Urs!

• 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.

## 2009-09-11

• 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 diffs so I need to fix it properly rather than just papering over the cracks.)

• A bit at lax natural transformation, which I really only mention since it's been discussed so much lately.
• Since Recently Revised works again, I've restored the link to it up above, from what it had been in June.
• Zoran Škoda: 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 Škoda: 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 Škoda: additions to deformation theory, derived algebraic geometry; created cotangent complex.

• Toby Bartels: I'm perfectly serious at (n,k)-transformation.

## 2009-09-09

• 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.

• 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 Škoda: 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.).

• Urs Schreiber

• 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 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.

## 2009-09-05

• Note spelling: Saunders Mac Lane.

• Zoran Škoda inserted and reminded of work of Rezk and Toën-Vezzosi on higher topos theory preceding the marvelous Lurie's work.

• Urs Schreiber

• 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 $\lambda_1=\rho_1$.

## 2009-09-04

• 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 Škoda: 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 Škoda: 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.

• 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 Škoda: 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 Škoda: 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.

• 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 Škoda: 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 ?

• Urs Schreiber

• 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 Škoda: 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 Škoda: additions to Ieke Moerdijk

• Tim Porter: I have removed the blue boxes as suggetsed by Urs (see below).

• Zoran Škoda: 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.

• Urs Schreiber

• 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

(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.

• Urs Schreiber: thanks! That’s very useful. i was hoping somebody would find the time to do that eventually. Great that you did it.

## 2009-09-03

• Todd Trimble: wrote article on tree.

• Zoran Škoda: 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 Škoda: 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: “Kantization” makes it sound like you are talking about Immanuel Kant — I think you should call it “Kanonization”.
• 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 Škoda: 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)

• 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).

• 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.

## 2009-09-02

• 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

• Mike Shulman: A bit more on displaying MathML at HowTo.

• Urs Schreiber

• Urs Schreiber

• 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)

• Mike Shulman

• Urs Schreiber

• Jon Awbrey added a stub and a few links on the subject of inquiry.

## 2009-09-01

• 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 Škoda: 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 Škoda: 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 Škoda: 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 Škoda: 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.

• 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 Škoda: 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 Škoda: 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).

• Urs Schreiber

• 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!?

• Andrew Stacey: I’ve looked for your question and can’t find it. I apologise if it’s been lost in the migration, but can you ask it again? If it’s technical, the forum might be a better place to ask it.
• 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? (^_^)

• Urs Schreiber: oops, you are right, I forgot that I am not exactly at GMT +0.
• Urs Schreiber

• moved the accumulated latest changes of last month to 2009 August changes (by renaming the last “latest changes” and then creating a new one)

category: meta

Revised on September 4, 2010 21:49:06 by Toby Bartels (173.190.156.19)