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Stream: learning: questions

Topic: Monad-like structure?

Mateo Torres-Ruiz (Jun 17 2025 at 08:31):

This might be a bit of a shot in the dark, but does the following ring a bell for anyone? I'm thinking of a monad-like structure with a functor $T:\mathcal{C}\times\mathcal{C}\to\mathcal{C}$, with unit $X\times Y\to T(X,Y)$ and bind $(X\times Y\to T(X'\times Y'))\to T(X\times Y)\to T(X'\times Y')$

Nathanael Arkor (Jun 17 2025 at 08:34):

This looks exactly like a [[relative monad]] whose root is the product functor $(\times) \colon \mathcal C \times \mathcal C \to \mathcal C$.

Morgan Rogers (he/him) (Jun 17 2025 at 08:35):

What is $T(X \times Y)$? Did you mean $T(X,Y)$ etc in the bind formula?

Nathanael Arkor (Jun 17 2025 at 08:35):

(Which would be an interesting example, because most examples of relative monads have fully faithful roots.)

Kenji Maillard (Jun 17 2025 at 10:25):

We employed this kind of relative monads over a product to try to give a systematic account of (binary) relational program logics over monadic programs in our paper The next 700 relational program logics .