If we have two $sSet$ enriched categories $C$ and $D$ is there a name for a $sSet-$enriched functor $G:C \rightarrow D$ such that the map $C(x,y) \rightarrow D(Gx,Gy)$ is a weak equivalence of simplicial sets? This could be a simplicial generalization of the concept of a fully faithful functor between $sSet-$enriched categories.
2026-03-27 14:30:41.1774621841
Generalization of fully faithful functors between $sSet-$enriched categories
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Many references write “homotopically fully faithful” for such an enriched functor.