nLab 2009 February changes

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.




  • Urs

  • Andrew

    • 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).





  • Mike: created n-fibration.

    Why do I think of the Beach Boys every time I read the word nn-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.






  • 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.

  • Urs

    • added Toën-Vezzosi proposal 2Vect:=Ch(Vect)Mod2Vect := Ch(Vect)-Mod to 2-vector space and created dg-category accompanying this


  • Mike:

  • Tim:

    • Added something to homotopy limit in part to provide a possible ‘old’ reference in reply to Urs and Mike below.
    • Started adding some summaries of results to group T-complex.
  • Toby Bartels:

  • 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

  • Mike Shulman:

    • 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).






  • 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.

  • David Roberts:




  • Andrew

    • Implemented the archive of latest changes (scroll down to the bottom of this page to get the link)
    • Added a fair bit more on Isbell Duality in Froelicher spaces. A few more general queries for those a little more versed in the lore of categories than me.


  • Eric

  • Andrew: continued with Froelicher spaces. In particular, laid out some of the details of the Isbell duality proof.

  • Urs

    • added as a further example the computation of holim(BHBGBH)H\\G//Hholim(\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:

    • Answered Urs’s question in a very long-winded way by adding lots of stuff to homotopy limit.
    • What would people think about rotating (i.e. archiving) the latest changes? every month, rather than every year? It’s pretty big right now and it will probably be immense by next December.


  • 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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Last revised on August 24, 2015 at 02:29:49. See the history of this page for a list of all contributions to it.