Enriched ∞-categories are equivalent to presentable module categories marked by an atomically generating family of representables.
On the tensor product of enriched $\infty$-categories
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abstract
We show that the tensor product of $\infty$-categories enriched in a suitable monoidal $\infty$-category preserves colimits in each variable, fixing a mistake in an earlier paper of Gepner and the author. We also prove that essentially surjective and fully faithful functors form a factorization system on enriched $\infty$-categories, and that the tensor product and internal hom are compatible with this.
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Enriched $\infty$-categories as marked module categories
Enriched ∞-categories are equivalent to presentable module categories marked by an atomically generating family of representables.