An equivalence between two models of $\infty$-categories of enriched presheaves

Abstract

Let $\mathcal{O}\to \mathrm{BM}$ be a $\mathrm{BM}$-operad that exhibits an $\infty$-category $\mathcal{D}$ as weakly bitensored over non-symmetric $\infty$-operads $\mathcal{V},\mathcal{W}$ and $\mathcal{C}$ a $\mathcal{V}$-enriched $\infty$-precategory. We construct an equivalence $${\mathrm{Fun}}_{\mathrm{Hin}}^{\mathcal{V}}(\mathcal{C},\mathcal{D})\simeq {\mathrm{Fun}}^{\mathcal{V}}(\mathcal{C},\mathcal{D})$$ of $\infty$-categories weakly right tensored over $\mathcal{W}$ between two different models of $\infty$-categories of $\mathcal{V}$-enriched functors, one introduced by Hinich and one constructed by us.