REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
ABSTRACT: Given a small abelian category A, by the Freyd-Mitchell Theorem, one can embed A exactly into a module category. Given a small additive category B, the category of finitely presented functors provides a way of embedding B into an abelian category Ab(B) that is universal. In the case B is abelian, Ab(B) is not in general equivalent to the original category B which is somewhat surprising. In this talk, I will explain in some detail how the category of finitely presented functors provides a way of constructing the universal solution Ab(B) which is commonly called the free abelian category on B. I will also recall the defect functor studied by Auslander and discuss its relationship to Ab(B) when B is an abelian category.
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu