English

The Homotopy Theory of $A_\infty$Categories

Algebraic Geometry 2026-01-21 v1 Algebraic Topology Category Theory

Abstract

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

Keywords

Cite

@article{arxiv.2408.05325,
  title  = {The Homotopy Theory of $A_\infty$Categories},
  author = {Mattia Ornaghi},
  journal= {arXiv preprint arXiv:2408.05325},
  year   = {2026}
}

Comments

49 pages, 5 figures