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arXiv · 2411.19751

Templicial nerve of an A-infinity category

Violeta Borges Marques·Arne Mertens
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Abstract

The framework of templicial vector spaces was put forth in arXiv:2302.02484v2 as a suitable generalization of simplicial sets in order to develop a theory of enriched quasi-categories, called quasi-categories in vector spaces. We construct a lift of Faonte's $A_{\infty}$-nerve arXiv:1312.2127v2 which lands in templicial vector spaces. Further, we show that when restricted to dg-categories, this nerve recovers the templicial dg-nerve of arXiv:2005.04778v4, and that the nerve of any $A_{\infty}$-category is a quasi-category in vector spaces.

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Violeta Borges Marques, Arne Mertens. 2024-11-29. Templicial nerve of an A-infinity category. https://arxiv.org/abs/2411.19751

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