#
nLab

enriched Reedy category

Contents
### Context

#### Model category theory

**model category**

## Definitions

## Morphisms

## Universal constructions

## Refinements

## Producing new model structures

## Presentation of $(\infty,1)$-categories

## Model structures

### for $\infty$-groupoids

for ∞-groupoids

### for equivariant $\infty$-groupoids

### for rational $\infty$-groupoids

### for rational equivariant $\infty$-groupoids

### for $n$-groupoids

### for $\infty$-groups

### for $\infty$-algebras

#### general

#### specific

### for stable/spectrum objects

### for $(\infty,1)$-categories

### for stable $(\infty,1)$-categories

### for $(\infty,1)$-operads

### for $(n,r)$-categories

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

#### 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.

## Definition

(…)

## 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.

(Angeltveit, theorem 4.7).

## References

Enriched Reedy categories were introduced in

The defintion is def. 4.1 there.

Last revised on March 28, 2012 at 04:58:07.
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