On effective descent $\mathcal{V}$-functors and familial descent morphisms

Abstract

We study effective descent $\mathcal{V}$-functors for cartesian monoidal categories $\mathcal{V}$ with finite limits. This study is carried out via the properties enjoyed by the $2$-functor $\mathcal{V}\mapsto \mathsf{Fam}(\mathcal{V})$, results about effective descent of bilimits of categories, and the fact that the enrichment $2$-functor preserves certain bilimits. Since these results rely on an understanding of (effective) descent morphisms in $\mathsf{Fam}(\mathcal{V})$, we briefly study those epimorphisms when $\mathcal{V}$ is a regular category.

17 p

References in corpus (2)

• Descent for internal multicategory functors
• The oplax limit of an enriched category

Cited by in corpus (1)

• Topological lax comma categories