Seminar of Algebra

Koszul duality is a phenomenon occurring widely throughout algebra and geometry, a classical example being the Bernstein–Gelfand–Gelfand correspondence which says that there is an equivalence between certain bounded derived categories. In more modern formulations of Koszul duality, due to Keller–Lefèvre and Positselski, the boundedness conditions are removed by replacing the derived category on one side by a "coderived" category, also called a derived category "of second kind". We will introduce these coderived categories and then show how further generalising Koszul duality leads to other, more exotic, derived categories of second kind.