In this paper we describe the homotopy category of the A_∞categories. To do that we introduce the notion of semi-free A_∞category, which plays the role of standard cofibration. Moreover, we define the non unital A_∞ (resp. DG)categories with cofibrant morphisms and we prove that any non unital A_∞ (resp. DG)category has a resolution of this kind.
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Mattia Ornaghi (2024) studied this question.
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