Comparing the homotopy categories of dg categories and of A-infinity categories - Paolo Stellari

This is a recorded version of the following talk from our "New Directions in Group Theory and Triangulated Categories" series. To receive updates about this series, or to suggest speakers (including yourself), please email me at [email protected].

More details about this seminar series are here -
https://sites.google.com/view/ndgttc/...
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94th Meeting of "New Directions in Group Theory and Triangulated Categories"

Date: May 9, 2024; Thursday

Time: 4 pm UK

Speaker: Paolo Stellari (Università degli Studi di Milano)

Title: Comparing the homotopy categories of dg categories and of A-infinity categories

Abstract: In this talk, we show that the homotopy category of (small) dg categories and the homotopy category of A_infty 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.