nLab enriched Reedy category

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

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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.

(Angeltveit, theorem 4.7).

Related concepts

• Reedy model structure, generalized Reedy model structure

References

Enriched Reedy categories were introduced in

• Vigleik Angeltveit, Enriched Reedy categories (arXiv:0612137)

The defintion is def. 4.1 there.