Dennis Clark

Triangulated Categories and Derived Functors


I will describe some of the technical details of derived categories, particularly the concepts of triangulated category and derived functor.  Since a derived category fails to be abelian, additional structure required to do work is provided by the concept of "distinguished triangles," an algebraic analog of the mapping cone construction of the homology long exact sequence in topology.  Also, I will describe derived functors in the derived category setting, in particular how they are essentially the orginal functor applied to complexes.  If time permits, I'll try to say a few words about the kinds of things that can be easily proven from this viewpoint.