Monads, Monoids, and Categories

Prev: Lawvere Theories

Prev: Lawvere Theories

Exercises

1. Derive unit and associativity laws for the tensor product defined as composition of endo-$1$-cells in a bicategory.
2. Check that monad laws for a monad in $\mathbf{Span}$ correspond to identity and associativity laws in the resulting category.
3. Show that a monad in $\mathbf{Prof}$ is an identity-on-objects functor.
4. What’s a monad algebra for a monad in $\mathbf{Span}$?