We prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital A∞ categories with respect to the corresponding classes of quasi-equivalences are all equivalent. Moreover we show that the last two localizations are equivalent to the corresponding quotients by the relation of being isomorphic in the cohomology of the A∞ category of A∞ functors. As an application we give a complete proof of a claim by Kontsevich stating that the category of internal Homs for two dg categories can be described as the category of strictly unital A∞ functors between them.
Localizations of the Category of A∞ Categories and Internal Homs / A. Canonaco, M. Ornaghi, P. Stellari. - In: DOCUMENTA MATHEMATICA. - ISSN 1431-0643. - 24(2019), pp. 2463-2492.
Localizations of the Category of A∞ Categories and Internal Homs
M. Ornaghi;P. Stellari
2019
Abstract
We prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital A∞ categories with respect to the corresponding classes of quasi-equivalences are all equivalent. Moreover we show that the last two localizations are equivalent to the corresponding quotients by the relation of being isomorphic in the cohomology of the A∞ category of A∞ functors. As an application we give a complete proof of a claim by Kontsevich stating that the category of internal Homs for two dg categories can be described as the category of strictly unital A∞ functors between them.File | Dimensione | Formato | |
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