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

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arxiv 2306.08115 v3 pith:CDUHD4J4 submitted 2023-06-13 math.CT math.AT

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keywords mathcalinftymathrmcategoriesenrichedequivalencemodelsweakly
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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.

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  1. Large condensation in enriched $\infty$-categories

    math.CT 2025-06 conditional novelty 6.0 of 10

    The paper extends condensation theory for higher symmetries from fusion n-categories to arbitrary enriched monoidal ∞-categories, using monoidal Eilenberg-Moore functors and iterated module categories.

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