A model structure on the category of A_∞-categories with strict morphisms

2025/06/28 by Mattia Ornaghi, Ornaghi, Mattia
Computer Science · Mathematics · #14F08 #18G70 #18N40 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.2506.22847

openalex publication_date 2025/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the category of (strictly unital) A_∞-categories, linear over a commutative ring R, with strict A_∞-morphisms has a cofibrantly generated model structure. In this model structure every object is fibrant and the cofibrant objects have cofibrant morphisms. As a consequence we prove that the semi-free A_∞-categories (resp. resolutions) are cofibrant objects (resp. resolution) in this model structure.

Citations

• Tensor product of A_∞-categories
• Localizations of the categories of A_∞ categories and internal Homs over a ring
• Sectorial descent for wrapped Fukaya categories
• Homotopy theory with *categories
• The homotopy theory of dg-categories and derived Morita theory
• Une structure de categorie de modeles de Quillen sur la categorie des dg-categories
• DG quotients of DG categories
• Homological algebra of homotopy algebras

Related

• The Homotopy Theory of A_∞Categories
• An inductive model structure for strict ∞-categories
• Semi-strictification of (∞, n)-categories
• From Hopf Algebras in Model Categories to Hopf Algebras in ∞-categories
• Model Structures on Exact Categories