2024/11/29 by Violeta Borges Marques, Marques, Violeta Borges, Arne Mertens +1
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2411.19751
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∞-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∞-category is a quasi-category in vector spaces.