2014/12/03 by Giovanni Faonte, Faonte, Giovanni · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1412.1255
openalex publication_date 2014/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove that Toen's derived enrichment of the model category of dg-categories defined by Tabuada, is computed by the dg-category of A-infinity functors. This approach was suggested by Kontsevich. We further put this construction into the framework of (infinity,2)-categories. Namely, we enhance the categories of dg and A-infinity categories, to (infinity,2)-categories. We prove that the (infinity,1)-truncation of to the (infinity,2)-category of dg-categories is a model for the simplicial localization at the model structure of Tabuada. As an application, we prove that the homotopy groups of the mapping space of endomorphisms at the identity functor in the (infinity,2)-category of A-infinity categories compute the Hochschild cohomology.