closed monoidal category module


A closed monoidal category module CC is a monoidal category module over a closed symmetric monoidal category VV such that the (left) action

:V×CC \otimes : V \times C \to C

extends to a two-variable adjunction. Such closed modules can be identified with VV-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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