Timeline for Equivariant colimit and equivariant functors
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 16, 2020 at 7:38 | vote | accept | Bryan Shih | ||
| Nov 15, 2020 at 18:53 | comment | added | Maxime Ramzi | @DylanWilson : yes, that's right - I was trying to come up with something more "intrinsic" somehow but I guess that works just as well | |
| Nov 15, 2020 at 18:48 | comment | added | Dylan Wilson | Another approach to equivariance of the colimit: wlog we may replace C with a cocomplete category (e.g. use the co-yoneda lemma, maybe enlarge the universe if you need to). Then colim: Fun(K, C)-->C is the same as Psh(K^{op})\otimes C---> Psh(pt)\otimes C where we use the tensor product in cocomplete categories. This reduces us to building equivariance on Psh(K)-->Psh(pt), but that follows by applying Psh(-): Cat---> (cocomplete Cat) to the functor K-->pt, which is manifestly equivariant. | |
| Nov 15, 2020 at 18:42 | history | answered | Maxime Ramzi | CC BY-SA 4.0 |