nLab
enriched Reedy category (changes)

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Idea

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for \infty-groupoids

for ∞-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

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

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

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

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

for (,1)(\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.

References

Definition

(…)

Properties

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

Proposition

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

(Angeltveit, theorem 4.7).

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)