Archive of changes made during February 2009. The substantive content of this page should not be altered. For past versions of this page beyond its own history, start here and work backwards.
edited action a bit more – but that entry is still not nice
extended geometric function theory
continued replying to Mike at hyperstructure
Created a request for help page. There are query boxes scattered all over the lab and I think that it ought to be a priority to answer these. A query on a page might be answerable by someone not an expert in what’s on that page (or even not interested in what’s on that page) - in fact, that’s highly likely. Flagging questions on this page (i.e., Latest Changes) is also less than optimal as it’s not clear who might be able to answer them (and probably not everyone checks this page). I freely admit that I’m doing this because no-one seems bothered in my questions on Froelicher spaces which are, in fact, more general category theory than specifics to Frölicher spaces.
I’ve added it to the sidebar (and taken off General Discussion).
created enriched functor category for completeness
added a bit more details and references concerning the SSet homotopy limit at weighted limit
after checking with Mike added details of the definition of homotopy limits in terms of weighted limits in the SSet-enriched context to weighted limit; also edited accordingly the section local definition at homotopy limit and created a section on weighted limits at representable functor
have a question at the end of weighted limit for the homotopy coherency experts
created weighted limit
added references to sheaf and simplicial set
Tim:
Mike: created n-fibration.
Why do I think of the Beach Boys every time I read the word $n$-fibrations? - Eric
Ronnie: over the last two days, created compositions in cubical sets which gives the basic definitions and axioms for cubical sets with compositions and connections, (and inverses), with the example of the cubical singular complex in mind.
Mike:
Mike:
Introduced the terminology strict homotopy limit by analogy with strict 2-limit.
Rearranged homotopy pullback to make it fit better with homotopy limit.
Mike: asked a question about horizontal categorification.
Tim: Added the construction of $\overline{W}$, the classifying space construction for simplicial groups to the entry for simplicial group.
created topological T-duality
created homotopy pullback
created weak equivalence
replied at dg-category
Ronnie Added entries on C. Ehresmann and on Grothendieck. The second probably should be expanded, but it has a link to a good account.
Tim: Asked a question in dg-category as to the degree of the differentials. We may need a convention on this.
Mike:
Incorporated the reference Tim suggested at homotopy limit.
Replied at strict 2-limit and comma category.
Tim:
Mike: Urs, in my biased opinion, the reference for the homotopy limit comparison that I find easiest to understand is my own paper (reference added). Of course the fact has been known for a long time; I don’t even know whether there’s any “original” source one could cite.
Urs: at homotopy limit I am asking for further details and/or literature on the “central theorem” which identified local and global definition
Added what I think is a more standard viewpoint to classifying space, although there are so many different meanings of that term.
Created comma object and started messing around with using SVG for diagrams instead of \array
. It’s more work but it sure does look nicer (in the output, anyway).
Urs: looks good! We should have at FAQ a brief instruction for how to proceed to produce such diagrams (which software to download, how to get nicely typeset labels, etc.)
Mike: I gave it a try, but I don’t have any great wisdom to impart; I just played around with the XML until it worked. If there is software that can do this for us that would be great (until someone manages to write an xypic-to-svg converter).
I like the edits at 2-limit and strict 2-limit, so I removed the comments (but anyone else with opinions, feel free to restart the discussion).
Naming question for large sheaf.
Answered at model structure on simplicial presheaves
have a question for Mike at model structure on simplicial presheaves
created Bousfield localization
created sheaves on large sites mainly to ask the question which I ask there
created model structure on simplicial presheaves, model structure on simplicial sheaves
Mike:
created Courant Lie algebroid
reacted to Toby’s remark at n-fold category by incorporating it and removing the query box
Mike:
fixed the mistake at interval object that Toby spotted and added a little bit of dicussion
added Berger-Moerdijk’s definition to interval object
Mike:
Replied to Toby at directed set, internal logic, and familial regularity and exactness.
Created weak limit.
Toby Bartels: Did some work on directed object, which I think should have half spun off to undirected object.
Tim:
Ronnie Brown: I edited the discussion in fibration to give a reference to work of P.R. Heath on operations of the paths on the base on the fibres, a groupoid operation up to homotopy.
Toby Bartels: I'm back! I'll be slowly catching up. So far, I've simply read latest changes and extended Andrew's navigation links for the archive. (So it looks like the sort of thing that daily updated websites create automatically using PHP, except that I did it all laboriously by hand!)
Jocelyn?: edited the product page to link to an interactive demonstration written to use the same notation as in product.
Mike: responded to all of David’s edits.
Edited anafunctor to clean up conditions on covers, and some explanations of what each one is for.
Created the page Grothendieck pretopology
Added mention of Dold fibration on the page fibration.
Mike:
Continued discussion with Urs at hyperstructure.
Moved thin to thin element in line with the naming convention that page names be singular nouns. Also added some other contexts in which “thinness” appears.
Urs:
added a “laboratory section” to hyperstructure in which I am proposing a formalization of the concept
created dagger category; started filling dagger compact category with content
Andrew: continued with Froelicher spaces. In particular, laid out some of the details of the Isbell duality proof.
added as a further example the computation of $holim(\mathbf{B}H \to \mathbf{B}G \leftarrow \mathbf{B}H) \simeq H \backslash\backslash G // H$ to homotopy limit
many thanks to Mike and Tim for all the further details at homotopy limit!
re Mike’s suggestion: yes, I’d be in favor of archiving the latest changes list here more frequently
Mike:
Andrew: After crashing the nLab 3 times I’ve finally managed to upload something on Frolicher spaces. Something is seriously wrong with my syntax - if no one’s taken pity on me and cleaned it up I’ll do so myself tomorrow. More importantly, I have a few queries for the more experienced categorists so I’d appreciate someone taking a look at those for me.
Urs: thanks, Mike, very useful. Is anything similar known for 3-categories?
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