nLab enriched monoidal model category

Idea

For $V$ a monoidal model category, a $V$-enriched monoidal model category is a model category equipped with

1. the structure of a monoidal model category,

2. the structure of a $V$-enriched model category,

3. the compatibility structure that makes the underlying monoidal and $V$-enriched structure a

   $V$-enriched monoidal category.

Examples

• For $V =$ $Set_{Qu}$ one typically speaks of simplicial monoidal model categories.