Timeline for If a monad in a 2-category admits a terminal resolution, does it admit an Eilenberg–Moore object?
Current License: CC BY-SA 4.0
7 events
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| Jul 25, 2022 at 16:54 | comment | added | Tim Campion | @varkor I agree about the historical interest. And it sure would be fun to see some weird pathological counterexample! | |
| Jul 25, 2022 at 16:49 | comment | added | varkor | Thanks, I agree with the conclusion now. I think it is essentially the statement of Theoreme 4.4 of Auderset's Adjonctions et monades au niveau des 2-catégories. I don't necessarily disagree that the condition I'm asking for is generally not the most appropriate condition to ask for, but it does seem like a natural one to consider (at least from a historical perspective). | |
| Jul 25, 2022 at 16:46 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Jul 25, 2022 at 16:41 | comment | added | Tim Campion | @varkor Hmmm... Yeah, I think I've been too hasty, and answered a slightly different question. I've edited above to reflect this. | |
| Jul 25, 2022 at 16:40 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Jul 25, 2022 at 16:29 | comment | added | varkor | Could you spell out why $\mathcal K$ admitting a terminal adjunction inducing $T$ for every monad $T$ is the same as admitting the specified right adjoint? Aren't the morphisms of the 2-category of adjunctions commutative squares, whereas the appropriate morphisms of "adjunctions inducing $T$" are commutative triangles? It's not obvious to me that the squares are forced to be trivial in this respect. | |
| Jul 25, 2022 at 16:19 | history | answered | Tim Campion | CC BY-SA 4.0 |