The Homotopy Theory of A∞categories

Mattia Ornaghi

doi:10.1093/imrn/rnaf127

The Homotopy Theory of A_∞categories

Mattia Ornaghi

Research output: Contribution to journal › Article › peer-review

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) A_∞ (resp. DG)categories with cofibrant morphisms and we prove that any (non-unital) A_∞ (resp. DG)category has a resolution of this kind.

Original language	English
Article number	rnaf127
Journal	International Mathematics Research Notices
Volume	2025
Issue number	11
DOIs	https://doi.org/10.1093/imrn/rnaf127
State	Published - 1 Jun 2025
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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The Homotopy Theory of A_∞categories

Abstract

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