MATH 7350 - Triangulated and Differential Graded Categories
Yuri Berest, spring 2017.
Triangulated categories were invented by J.-L. Verdier in the early sixties as an appropriate language for formulating Grothendieck's duality theory in algebraic geometry. Since then they have become a standard tool in homological algebra and found applications in many areas, far beyond algebraic geometry. However, it has been known for a long time that basic axioms of triangulated categories have some intrinsic deficiency and need to be 'enhanced'. This course will be an introduction to the theory of differential graded (DG) and A-infinity categories which seem to provide such an enhancement. We will start with a quick overview of basic homological algebra which should provide enough background for understanding the main part of the course. In the second part, we will focus on various applications of DG categories in algebra and geometry. In a sense, this will be a continuation of my course on "Homotopical Algebra" (MATH 7400) that I taught in Fall 2014.