Timeline for What is the relationship between $O_G$-parameterized $\infty$-categories and $\infty$-categories enriched in $Top_G$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 11, 2018 at 14:28 | answer | added | Tim Campion | timeline score: 3 | |
| Jun 11, 2018 at 13:35 | comment | added | Tim Campion | @DylanWilson I think the edit gives an idea how the comparison should go. I wasn't sure before. | |
| Jun 11, 2018 at 12:56 | comment | added | Tim Campion | Okay, maybe the better comparison is to categories internal to $Top_G$. | |
| Jun 11, 2018 at 12:54 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Jun 11, 2018 at 6:23 | comment | added | Denis Nardin | Yeah, not all objects over $G/e$ will come by restriction from an object over $G/G$ in a $G$-parametrized category (silly example: take $EG$ as a $G$-parametrized groupoid). I think you might have some hope for full faithfulness though | |
| Jun 11, 2018 at 2:48 | comment | added | Marc Hoyois | From an ∞-category enriched in presheaves on $C$ you should get a presheaf of ∞-categories on $C$ by changing the enrichment via the evaluation functors. This construction is a right adjoint functor, and naively I would expect it to be fully faithful but not essentially surjective. | |
| Jun 10, 2018 at 23:30 | comment | added | Dylan Wilson | Do you have something in mind in the 1-categorical case? Like a comparison between categories opfibered over O_G^{op} and categories enriched in presheaves of sets on the orbit category? My first guess is that these things (in the 1-categorical and infty-categorical cases) should be quite different. Maybe categories internal to G-spaces gets you closer? But they still feel different. | |
| Jun 10, 2018 at 21:20 | history | asked | Tim Campion | CC BY-SA 4.0 |