The Homotopy Theory of A_∞Categories

2024/08/09 by Mattia Ornaghi, Ornaghi, Mattia
Decision Sciences · Mathematics · #14F08 #18E35 #18G70 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2408.05325

openalex publication_date 2024/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we describe the homotopy category of the A_∞categories. To do that we introduce the notion of semi-free A_∞category, which plays the role of standard cofibration. Moreover, we define the non unital A_∞ (resp. DG)categories with cofibrant morphisms and we prove that any non unital A_∞ (resp. DG)category has a resolution of this kind.

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