{"title":"The Homotopy Theory of $A_\\infty$Categories","authors":"Mattia Ornaghi","doi":"arxiv-2408.05325","DOIUrl":null,"url":null,"abstract":"In this paper we describe the homotopy category of the $A_\\infty$categories.\nTo do that we introduce the notion of semi-free $A_\\infty$category, which plays\nthe role of standard cofibration. Moreover, we define the non unital $A_\\infty$\n(resp. DG)categories with cofibrant morphisms and we prove that any non unital\n$A_\\infty$ (resp. DG)category has a resolution of this kind.","PeriodicalId":501135,"journal":{"name":"arXiv - MATH - Category Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Category Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.05325","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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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