NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT

REPRESENTATION THEORY AND RELATED TOPICS SEMINAR


  Jeremy Russell
(Ewing, NJ)


Embedding an Abelian Category into the Free Abelian Category

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.


January 22, 2015
4:30 - 5:30
(Notice unusual time)
511 Lake Hall


For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky alexmart >at< neu >dot< edu