In this paper we describe the homotopy category of the (unital and strictly unital) 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) (resp. DG) A∞-categories with cofibrant morphisms and we prove that any (non-unital) A∞-(resp. DG)category has a resolution of this kind.
The Homotopy Theory of A∞categories / M. Ornaghi. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2025:11(2025 Jul), pp. rnaf127.1-rnaf127.59. [10.1093/imrn/rnaf127]
The Homotopy Theory of A∞categories
M. Ornaghi
2025
Abstract
In this paper we describe the homotopy category of the (unital and strictly unital) 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) (resp. DG) A∞-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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