Timeline for Intuition behind Mac Lane's "subdivision category"
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 6 at 12:39 | history | edited | darij grinberg | CC BY-SA 4.0 |
added 3 characters in body
|
| Sep 6 at 11:51 | answer | added | Peter LeFanu Lumsdaine | timeline score: 5 | |
| Jan 10, 2020 at 23:25 | vote | accept | fosco | ||
| Sep 5, 2019 at 21:46 | comment | added | fosco | I don't see why you say other : afaicu what Tim is pointing out is that you can consider the subdivision category as the image of $C$ under a functor, but this functor is better appreciated at the level of $\infty$-categories, because at that level it's a subdivision functor $$X\mapsto \text{sd}(X) = \int^n X_n\times N([n]\cup [n]^{op} )$$ | |
| Sep 4, 2019 at 3:24 | comment | added | Mike Shulman | Yes, I think clearly this category is cooked up precisely so as to make the theorem true. But as Tim's answer points out, there are also other categories that suffice to make the same theorem true and that are less ad hoc. | |
| Sep 2, 2019 at 21:13 | answer | added | Tim Campion | timeline score: 3 | |
| Sep 2, 2019 at 15:52 | comment | added | Dmitri Pavlov | I cannot possibly know what Mac Lane thought, but it would seem to me that this definition is specifically designed to make the cited theorem about colimits and coends true. The very special form of the indexing category F^§ allows us to compute the colimit over F^§ as the coequalizer of two maps between the corresponding coproducts, and from there it is easy to get to coends. | |
| Sep 2, 2019 at 15:40 | history | asked | fosco | CC BY-SA 4.0 |