Geodesic
Localizations of the Category of $A_\infty$ Categories and Internal Homs
Documenta mathematica, Tome 24 (2019), pp. 2463-2492.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital $A_\infty$ 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 $A_\infty$ category of $A_\infty$ 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 $A_\infty$ functors between them.
Classification : 18D20, 18E35, 18G55, 57T30
Keywords: dg categories, \(A_\infty\) categories 
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     author = {Canonaco, Alberto and Ornaghi, Mattia and Stellari, Paolo},
     title = {Localizations of the {Category} of {\(A_\infty\)} {Categories} and {Internal} {Homs}},
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Canonaco, Alberto; Ornaghi, Mattia; Stellari, Paolo. Localizations of the Category of \(A_\infty\) Categories and Internal Homs. Documenta mathematica, Tome 24 (2019), pp. 2463-2492. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a4/