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

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 $\mathcal{V}\mapsto \mathsf{F}\mathsf{a}\mathsf{m}(\mathcal{V})$, 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 $\mathsf{F}\mathsf{a}\mathsf{m}(\mathcal{V})$, we briefly study those epimorphisms when $\mathcal{V}$ is a regular category.