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arXiv · 2408.05325

The Homotopy Theory of $A_\infty$Categories

Mattia Ornaghi
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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.

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Mattia Ornaghi. 2024-08-09. The Homotopy Theory of $A_\infty$Categories. https://doi.org/10.1093/imrn%2Frnaf127

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