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Hi again,
In Module category, it says:
Let ℳ be a monoidal category and Bℳ its delooping as a bicategory. A (left) module category is then simply a 2-functor Bℳ→𝒞𝒶𝓉.
Further expanding this definition, we have the following data:
- A category 𝒞
- A functor −▹−:𝒞×ℳ→ℳ
- A natural isomorphism αA,B,X:A▹(B▹X)→(A⊗B)▹X satisfying a pentagon axiom involving the associator of ℳ
Shouldn’t item 2 be “A functor −▹−:ℳ×𝒞→𝒞 “?
Yes, fixed now.
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