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Stream: learning: questions

Topic: strange monoids

Joe Moeller (Nov 22 2024 at 19:22):

I'm working with something that almost looks like a monoid, but the operation has the form $A \times F(A) \to A$ for an endofunctor $F \colon C \to C$. Also, there's a forgetful functor $U \colon C \to D$, and $UA$ is a monoid in $D$. Does this sort of structure have a name?

Nathanael Arkor (Nov 22 2024 at 19:54):

Have you checked whether ${-} \times F({-})$ forms a (skew) monoidal structure? Lack–Street's Monads and warpings might be a relevant reference.

Joe Moeller (Nov 26 2024 at 04:13):

Yeah, this might be it. Thanks!