The paper establishes graded functor categories and graded bifunctors over arbitrary monoidal V by working in V-graded categories, generalizing enriched categories and actegories, with examples including V-graded modules and presheaf categories.
Mac Lane, Categories for the working mathematician , second ed., Springer- Verlag, 1998
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V-graded categories and V-W-bigraded categories: Functor categories and bifunctors over non-symmetric bases
The paper establishes graded functor categories and graded bifunctors over arbitrary monoidal V by working in V-graded categories, generalizing enriched categories and actegories, with examples including V-graded modules and presheaf categories.