Contemts

model category

## Model structures

for ∞-groupoids

### for $(\infty,1)$-sheaves / $\infty$-stacks

#### Enriched category theory

enriched category theory

# Contemts

## Definition

In enriched model category theory, an enriched Quillen adjunction is an enriched adjunction whose underlying ordinary adjunction is a Quillen adjunction between ordinary model categories.

Here “underlying” refers to the underlying ordinary category $C_0$ of any $V$-enriched category, defined by $C_0(x,y) = V(I,C(x,y))$. (Recall that an enriched model category is an enriched category, together with a model structure on its underlying ordinary category, and some compatibility conditions.)

## Special cases

A special role is played by sSet-enriched Quillen adjunctions, for the standard model structure on simplicial sets. See simplicial Quillen adjunction for more on that.

Last revised on September 20, 2018 at 13:20:19. See the history of this page for a list of all contributions to it.