Timeline for A right adjoint preserves Phi-colimits if and only if the left adjoint does what?

Current License: CC BY-SA 4.0

10 events

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Jun 24, 2023 at 17:54	comment	added	varkor		@MaximeRamzi: yes, I'm really interested in the question from a conceptual perspective, so presentability assumptions are stronger than I'm hoping for.
Jun 24, 2023 at 16:37	comment	added	Maxime Ramzi		Not exactly - the case where $C$ is $\omega$-presentable and $\Phi$ = filtered colimits is spelled out. For example there is a more general criterion for the same $\Phi$ but when $C$ is only compactly assembled, which is weaker than compactly generated. But you might also be interested in different $\Phi$
Jun 24, 2023 at 16:31	comment	added	varkor		@MaximeRamzi: the case where $\mathbf C$ is presentable is already spelled out in my question.
Jun 24, 2023 at 16:21	comment	added	Maxime Ramzi		Would an answer in the case where C and D are presentable be satisfactory ? Or is that too restrictive ?
Jun 24, 2023 at 14:00	history	rollback	varkor		Rollback to Revision 1
Jun 24, 2023 at 13:38	history	edited	varkor	CC BY-SA 4.0	added 53 characters in body
Jun 24, 2023 at 13:19	history	edited	varkor	CC BY-SA 4.0	added 53 characters in body
Jul 13, 2022 at 15:44	comment	added	varkor		@SimonHenry: thanks for pointing that out. I found essentially this question in the context of geometric morphisms. An answer to one will most likely answer the other, but I think it's useful to phrase it more generally, so I'll keep my question open.
Jul 13, 2022 at 15:38	comment	added	Simon Henry		The dual situation of a left adjoint functor that preserves finite limits has been considered a lot (The geometric morphisms between topos) and I have never seen a condition only involving the right adjoint functors.
Jul 13, 2022 at 11:57	history	asked	varkor	CC BY-SA 4.0