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The Homotopy Theory of $A_\infty$Categories
Published 9 Aug 2024 in math.AG, math.AT, and math.CT | (2408.05325v1)
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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