Corpus ID: 119684610

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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