Timeline for Algebras for products or limits of monads
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 11, 2023 at 7:41 | answer | added | varkor | timeline score: 2 | |
| Jul 18, 2020 at 15:05 | comment | added | Simon Henry | @TimCampion That's interesting. There are several way to construct a category Mnd of monads, which one are you referring to in your comment ? is it equivalent to the full subcategory of $\mathbf{Cat}^\to$ of monadic right adjoint functors ? I have the impression that the underlying idea of your comment actually say something about colimits of monads instead of limits (due to a hidden opposite category in the convention), for which it is indeed easy to describe the category of algebras... | |
| Jul 17, 2020 at 21:44 | comment | added | Tim Campion | By the formal theory of monads, the 2-functor $Alg: Mnd \to Cat$ is right 2-adjoint to the 2-functor which sends a category to the identity monad on it (here $Mnd$ is the 2-category of monads in $Cat$). So perhaps one should ask which limits in $Mnd(C)$ are also limits in the larger 2-category $Mnd$. I'm a bit confused, though, because there's some weirdness about which direction the coherence 2-cell points in the definition of a 1-morphism of monads, which might not line up properly for $Mnd(C)$ to actually be a sub-2-category of $Mnd$. | |
| Jul 7, 2020 at 16:43 | history | asked | Simon Henry | CC BY-SA 4.0 |