In this talk, we show that the homotopy category of (small) dg categories and the homotopy category of A∞-categories are equivalent (even from a higher categorical viewpoint). We will discuss several issues related to the various notions of unity and provide several applications. The main ones are about the uniqueness of enhancements for triangulated categories and a full proof of a claim by Kontsevich and Keller concerning a description of the category of internal Homs for dg categories.
This is joint work with A. Canonaco and M. Ornaghi.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
