Enriched homotopy-coherent structures

Hongyi Chu; Rune Haugseng

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arXiv · 2308.11502

Enriched homotopy-coherent structures

Hongyi Chu·Rune Haugseng

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Abstract

We introduce a general notion of enrichment for homotopy-coherent algebraic structures described by Segal conditions, using the framework of "algebraic patterns" developed in our previous work. This recovers several known examples of enriched structures, including enriched $\infty$-categories, enriched $\infty$-operads, and enriched $\infty$-properads. As new examples we discuss enriched modular $\infty$-operads, enriched $n$-fold $\infty$-categories, and a non-iterative definition of enriched $(\infty,n)$-categories.

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Hongyi Chu, Rune Haugseng. 2023-08-22. Enriched homotopy-coherent structures. https://arxiv.org/abs/2308.11502

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