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    • CommentRowNumber1.
    • CommentAuthorjesuslop
    • CommentTimeAug 18th 2018
    • (edited Aug 18th 2018)

    Hi again,

    In Module category, it says:

    Let \mathcal{M} be a monoidal category and BB\mathcal{M} its delooping as a bicategory. A (left) module category is then simply a 2-functor B𝒞𝒶𝓉B\mathcal{M} \to \mathcal{Cat}.

    Further expanding this definition, we have the following data:

    • A category 𝒞\mathcal{C}
    • A functor :𝒞×- \triangleright -\colon \mathcal{C} \times \mathcal{M} \to \mathcal{M}
    • A natural isomorphism α A,B,X:A(BX)(AB)X\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 :×𝒞𝒞- \triangleright -\colon \mathcal{M} \times \mathcal{C} \to \mathcal{C} “?

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 18th 2018

    Yes, fixed now.

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