arXiv Analytics

Sign in

arXiv:1312.2127 [math.AT]AbstractReferencesReviewsResources

Simplicial nerve of an A-infinity category

Giovanni Faonte

Published 2013-12-07, updated 2015-09-08Version 2

In this paper we introduce a functor, called the simplicial nerve of an A-infinity category, defined on the category of (small) A-infinity categories with values in simplicial sets. We prove that the simplicial nerve of any A-infinity category is an infinity category. This construction extends functorially the nerve construction for differential graded categories proposed by J.Lurie in Higher Algebra. We prove that if a differential graded category is pretriangulated in the sense of A.I.Bondal-M.Kapranov, then its nerve is a stable infinity category in the sense of J.Lurie.

Comments: 47 pages, References Added
Categories: math.AT, math.CT
Related articles: Most relevant | Search more
arXiv:2207.14608 [math.AT] (Published 2022-07-29)
An $\infty$-categorical localisation functor for diagrams of simplicial sets
arXiv:2111.06512 [math.AT] (Published 2021-11-12, updated 2022-03-31)
Generalizing quasi-categories via model structures on simplicial sets
arXiv:2501.03116 [math.AT] (Published 2025-01-06)
Poincaré-Birkhoff-Witt Theorems in Higher Algebra

Links

Toolbox