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Results tagged with monads
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user 4262
12
votes
Accepted
Eilenberg–Moore algebras in terms of Kleisli ones
One nice result is Street's theorem 14 in The formal theory of monads, generalized in Elementary cosmoi, which says that $C^T$ is isomorphic to the full subcategory of $[(C_T)^{\mathrm{op}}, \mathrm{Set … Maybe try Kelly & Power, Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads, JPAA 89 (1993). …
- 3,622
15
votes
Accepted
Any example of a non-strong monad?
Here is a class of examples different to Tom's: if your underlying monoidal category C is closed, then a strong monad on C is the same as a C-enriched monad, i.e. one that respects the enrichment of C …
- 3,622
8
votes
Accepted
Monad arising from operad
The answer is no, and it is explained in Appendix C of Leinster's book Higher Operads, Higher Categories.
Briefly, a 'plain operad', for Leinster, is a non-symmetric operad in Set; a T-operad for T t …
- 3,622
7
votes
Relation between monads, operads and algebraic theories
Apart from Todd's recommendations, which I'd second, for monads and Lawvere theories there is Nishizawa and Power, Lawvere theories enriched over a general base, JPAA 213, 2009, and the references therein …
- 3,622