Timeline for Lifting adjunctions along a localisation of 2-categories
Current License: CC BY-SA 4.0
8 events
when toggle format | what | by | license | comment | |
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Apr 28, 2023 at 22:48 | comment | added | Kevin Carlson | That's the idea, but the flexible objects will be easier to get at for the reasons you mention. | |
Apr 28, 2023 at 15:59 | comment | added | Nico | @KevinArlin The coflexible objects should be exactly the fibrant objects in the injective model structure, i.e. the model structure which I get when I view $U_s$ as a left $Cat$-enriched adjoint and lift along it, right? | |
Apr 28, 2023 at 15:54 | comment | added | Kevin Carlson | It’s not clear to me that you need to worry about the comonad when the monad is also around. | |
Apr 28, 2023 at 14:26 | comment | added | Nico | @KevinArlin I have gotten the impression that it is in general harder to lift a model structure along a left adjoint. There are always a lot of set theoretic smallness conditions which I do not really understand, but I think they are not completely symmetric :/ | |
Apr 28, 2023 at 14:25 | comment | added | Nico | @KevinArlin Yes, I think your right. I need exactly the dual of Lack's paper. I have read somewhere that strict indexed categories are Cat-enriched comonadic above $[\mathcal S_0,Cat]$, but I do not know enoough to check that everything else also dualizes | |
Apr 20, 2023 at 4:40 | comment | added | Kevin Carlson | Oh, I think what’s weird here is that the right adjoint is extra, but otherwise everything follows a familiar story in 2-algebra: fibrations are pseudo-algebras for the “comma” 2-monad on Cat/S and split fibrations are strict algebras, so the free split fibration on a fibration will have every Cartesian map out iso to a split one and dually, for the cofree split fibration. | |
Apr 20, 2023 at 4:29 | comment | added | Kevin Carlson | I don’t really know, but could fibrations in S be something like pseudo-coalgebras for a 2-comonad on Cat/S, with split fibrations the strict algebras? Then the universal splitting of a fibration ought to be coflexible, with every Cartesian functor into it isomorphic to a strict one. | |
Apr 13, 2023 at 13:19 | history | asked | Nico | CC BY-SA 4.0 |