# Localizations of the category of $A_\infty$ categories and internal Homs

@article{Canonaco2018LocalizationsOT, title={Localizations of the category of \$A\_\infty\$ categories and internal Homs}, author={A. Canonaco and M. Ornaghi and P. Stellari}, journal={arXiv: Algebraic Geometry}, year={2018} }

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… Expand

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