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arXiv · 2006.09408

The coalgebraic enrichment of algebras in higher categories

Maximilien Péroux
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Abstract

We prove that given $\mathcal{C}$ a presentably symmetric monoidal $\infty$-category, and any essentially small $\infty$-operad $\mathcal{O}$, the $\infty$-category of $\mathcal{O}$-algebras in $\mathcal{C}$ is enriched, tensored and cotensored over the presentably symmetric monoidal $\infty$-category of $\mathcal{O}$-coalgebras in $\mathcal{C}$. We provide a higher categorical analogue of the universal measuring coalgebra. For categories in the usual sense, the result was proved by Hyland, L\'{o}pez Franco, and Vasilakopoulou.

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Maximilien Péroux. 2020-06-16. The coalgebraic enrichment of algebras in higher categories. https://arxiv.org/abs/2006.09408

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