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1. • CommentRowNumber1.
   • CommentAuthorjesuslop
   • CommentTimeAug 18th 2018
   • (edited Aug 18th 2018)
   • PermaLink
   Author: jesuslop
   Format: MarkdownItexHi again, In [Module category](https://ncatlab.org/nlab/show/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 $- \triangleright -\colon \mathcal{M} \times \mathcal{C} \to \mathcal{C}$ "?

   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 $- \triangleright -\colon \mathcal{M} \times \mathcal{C} \to \mathcal{C}$ “?

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeAug 18th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexYes, fixed now.

   Yes, fixed now.