On the tensor product of enriched $\infty$-categories

Rune Haugseng

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arXiv · 2311.13362

On the tensor product of enriched $\infty$-categories

Rune Haugseng

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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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Rune Haugseng. 2023-11-22. On the tensor product of enriched $\infty$-categories. https://arxiv.org/abs/2311.13362

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