The Homotopy Theory of $A_\infty$Categories
Abstract
In this paper we describe the homotopy category of the $A_\infty$categories. To do that we introduce the notion of semi-free $A_\infty$category, which plays the role of standard cofibration. Moreover, we define the non unital $A_\infty$ (resp. DG)categories with cofibrant morphisms and we prove that any non unital $A_\infty$ (resp. DG)category has a resolution of this kind.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.05325
- arXiv:
- arXiv:2408.05325
- Bibcode:
- 2024arXiv240805325O
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Algebraic Topology;
- Mathematics - Category Theory;
- 14F08;
- 18E35;
- 18G70
- E-Print:
- 49 pages, 5 figures