Timeline for A Whitehead theorem for 3-categories
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 5, 2020 at 3:26 | comment | added | Mike Shulman | By "3-category", "3-functor", etc. do you mean weak ones or strict ones? Traditionally in "low-dimensional higher category theory" the words "2-category" and "3-category" mean the strict versions, with "bicategory" and "tricategory" for the weak ones. | |
| May 4, 2020 at 15:37 | history | edited | JeCl | CC BY-SA 4.0 |
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| Apr 26, 2020 at 8:26 | comment | added | Marc Hoyois | There should be such a theorem for $n$-categories for any $n$ (with condition 1 exactly as you stated), in fact even for $(\infty,n)$-categories. There are several equivalent definitions of the latter, and I think this theorem is more or less straightforward using Barwick's complete $n$-fold Segal spaces (see section 14 in arxiv.org/pdf/1112.0040.pdf for the definition). | |
| Apr 26, 2020 at 6:26 | comment | added | David Roberts♦ | That said, I would guess the theorem is true, for the correct definitions of all the things you mention. The trick is more getting the definition completely written down. | |
| Apr 26, 2020 at 6:25 | comment | added | David Roberts♦ | Regarding your last comment, this might be the difference between an adjoint equivalence, and one where the various data are not chosen to be coherent, or even only postulated to exist. I would start with Nick Gurski's book Coherence in Three-Dimensional Category Theory, or other of his work. The paper Biequivalences in tricategories is not enough, but might give you hints: tac.mta.ca/tac/volumes/26/14/26-14abs.html | |
| Apr 26, 2020 at 5:52 | history | asked | JeCl | CC BY-SA 4.0 |