Short Course

Introduction to Differential Graded Categories

Gonçalo Tabuada

(Université Denis Diderot - Paris VII)

September 25-27, 2006

Abstract: This course will be an introduction to the homotopy theory of differential graded categories and applications. Here is a brief outline:

• Motivation for the study of DG cats.
• Description of the quasi-equivalence model structure on DG cats.
• Description of the homotopy relation and the DG-quotient. Toen's description of the Dwyer-Kan simplicial localization.
• The Morita model structure. Reinterpretation of the triangulated envelope of Bondal and Kapranov.
• The universal additive invariant of a DG-cat.