Timeline for Coequalizers in stable (infinity,1)-categories
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2013 at 1:07 | comment | added | Dylan Wilson | @MikeShulman I sent you an email with a write up. If it's up to par, I'll post it as an answer here (if I can figure out how to make the diagrams...) | |
| Jul 23, 2013 at 19:45 | comment | added | Dylan Wilson | Writing up lots and lots of details, will post a little later today. | |
| Jul 23, 2013 at 17:20 | comment | added | Mike Shulman | Can you explain how your "construction" gives a map $\mathrm{Fun}(\mathrm{Fork},\mathcal{C}) \to \mathrm{Fun}(\Delta^1\vee\Delta^1,\mathcal{C})$ and not just an operation on objects? And what exactly is this "inverse functor"? Finally, yes, I would very much appreciate anything to make this more rigorous. | |
| Jul 23, 2013 at 17:13 | comment | added | Mike Shulman | For me, in the ordinary case, identifying the coequalizer with that pushout "by checking universal properties" would go like "the pushout represents pairs $h,k:Y\to Z$ such that $h(g,1) = k(f,1)$, i.e. $h g = k f$ and $h = k$, hence just a single map $h:Y\to Z$ such that $h g = h f$." I very much appreciate your word "reckless" for calling any $(\infty,1)$-categorical proof "the same" as this. (-: | |
| Jul 22, 2013 at 23:01 | comment | added | Dylan Wilson | Hi five! I can delete mine if you like, I'm only keeping it up for now cuz it has references- but if Mike doesn't need them I'll get rid of it. | |
| Jul 22, 2013 at 22:57 | comment | added | Omar Antolín-Camarena | Looks like we wrote pretty much the same answer, too. | |
| Jul 22, 2013 at 18:44 | comment | added | Dylan Wilson | Whoops, didn't notice someone had already answered. | |
| Jul 22, 2013 at 18:43 | history | answered | Dylan Wilson | CC BY-SA 3.0 |