# nLab enriched Reedy category

model category

## Model structures

for ∞-groupoids

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

#### Enriched category theory

enriched category theory

# Contents

## Idea

The notion of enriched Reedy category is a combination of that of Reedy category and enriched category.

The main motivation for studying Reedy categories is that they induce Reedy model structures on functor categories.

The motivation for studying enriched Reedy categories is that they induced enriched Reedy model structures on enriched functor categories.

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## Properties

Let $\mathcal{V}$ be a monoidal model category. Let $\mathcal{A}$ be a $\mathcal{V}$-enriched Reedy category and let $\mathcal{E}$ be a $\mathcal{V}$-enriched model category. Write $[\mathcal{A}, \mathcal{C}]$ for the enriched functor category.

###### Proposition

The enriched Reedy model structure on $[\mathcal{A}, \mathcal{C}]$ exists and is a $\mathcal{V}$-enriched model category.

## References

Enriched Reedy categories were introduced in

The defintion is def. 4.1 there.

Revised on March 28, 2012 04:58:07 by Urs Schreiber (82.169.65.155)