closed monoidal category module

A *closed monoidal category module* $C$ is a monoidal category module over a closed symmetric monoidal category $V$ such that the (left) action

$\otimes : V \times C \to C$

extends to a two-variable adjunction. Such closed modules can be identified with $V$-enriched categories having powers and copowers.

This is in chapter 4 of

- M. Hovey,
*Model Categories*, volume 63 of*Mathematical Surveys and Monographs*, AMS, 1999.

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