on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
on algebras over an operad, on modules over an algebra over an operad
on dendroidal sets, for dendroidal complete Segal spaces, for dendroidal Cartesian fibrations
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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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.
The enriched Reedy model structure on $[\mathcal{A}, \mathcal{C}]$ exists and is a $\mathcal{V}$-enriched model category.
Enriched Reedy categories were introduced in
The defintion is def. 4.1 there.