Timeline for Concrete example of $\infty$-categories
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 27, 2012 at 3:07 | comment | added | Tim Campion | available from his webpage web.science.mq.edu.au/~mbatanin/papers.html . But that preprint is pretty old, and my impression as a non-expert is that Batanin and Weber's work over the last decade doesn't really work through stuff combinatorially... I would really love for someone to explain to me what's wrong or unclear with this or any other of my above statements. | |
| May 27, 2012 at 3:03 | comment | added | Tim Campion | It's hard for a non-expert to gauge just what what role computads play -- Batanin erroneously claimed (I think in the paper mentioned above?) that they form a presheaf category; this was corrected by Makkai and Zawadowski in their paper "The category of 3-computads is not cartesian closed". In Leinster's book, I think one roughly finds the idea "computads = many-in/many-out version of opetopes", and the fact that they don't form a presheaf category is taken as a sort of "no-go" theorem for using them in an "operadic" way. But Batanin has some sort of preprint saying that they're still useful | |
| May 27, 2012 at 2:57 | comment | added | Tim Campion | I think the original reference should be Batanin's paper "Monoidal Globular Categories as a natural setting..." (which unfortunately doesn't seem to be freely available). Somewhere in among the various categories of pasting diagrams and so forth in Leinster's book "Higher Operads, Higher Categories" (freely available on his website) lies this particular object, but I'm not sure exactly where. Street's computads (see the nlab page) are supposed to enable explicit combinatorial, generators-and-relations treatment of higher categories. | |
| Sep 1, 2011 at 16:06 | comment | added | Giorgio Mossa | @tomleinster This should be the free $\infty$-category on the terminal globular set, shouldn't it? Is there any reference in which there's the explicit combinatorial description of this weak category? | |
| Aug 26, 2011 at 19:55 | history | edited | Tom Leinster | CC BY-SA 3.0 |
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| Aug 26, 2011 at 19:49 | history | answered | Tom Leinster | CC BY-SA 3.0 |