# nLab enriched Reedy category

Contents

### Context

#### Model category theory

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 $\infty$-algebras

specific $\infty$-algebras

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

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.

Last revised on March 28, 2012 at 04:58:07. See the history of this page for a list of all contributions to it.