Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Hi again,
In Module category, it says:
Let $\mathcal{M}$ be a monoidal category and $B\mathcal{M}$ its delooping as a bicategory. A (left) module category is then simply a 2-functor $B\mathcal{M} \to \mathcal{Cat}$.
Further expanding this definition, we have the following data:
- A category $\mathcal{C}$
- A functor $- \triangleright -\colon \mathcal{C} \times \mathcal{M} \to \mathcal{M}$
- A natural isomorphism $\alpha_{A,B,X}\colon A \triangleright (B \triangleright X) \to (A \otimes B) \triangleright X$ satisfying a pentagon axiom involving the associator of $\mathcal{M}$
Shouldn’t item 2 be “A functor $- \triangleright -\colon \mathcal{M} \times \mathcal{C} \to \mathcal{C}$ “?
Yes, fixed now.
1 to 2 of 2