Abstract
For any suitable base category $\mathcal{V} $, we find that $\mathcal{V} $-fully faithful lax epimorphisms in $\mathcal{V} $-$\mathsf{Cat} $ are precisely those $\mathcal{V}$-functors $F \colon \mathcal{A} \to \mathcal{B}$ whose induced $\mathcal{V} $-functors $\mathsf{Cauchy} F \colon \mathsf{Cauchy} \mathcal{A} \to \mathsf{Cauchy} \mathcal{B} $ between the Cauchy completions are equivalences. For the case
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