Localizations of the Category of ACategories and Internal Homs

Alberto Canonaco, Mattia Ornaghi, Paolo Stellari

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital Acategories 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 Acategory of Afunctors. 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 Afunctors between them.

Original languageEnglish
Pages (from-to)2463-2492
Number of pages30
JournalDocumenta Mathematica
StatePublished - 1 Jan 2019


  • Acategories
  • Dg categories

ASJC Scopus subject areas

  • Mathematics (all)


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