nLab
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

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

Refererences

This is in chapter 4 of

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