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