THEORY AND RELATED TOPICS SEMINAR
ABSTRACT: The concept of morphisms determined by objects was introduced by Auslander in 1978. We generalize it to the notion of morphisms determined by subcategories and study the existence and uniqueness of minimal right determiners in various categories. In particular, in a Hom-finite, hereditary abelian category with enough projective objects, we prove that Auslander-Reiten-Smalo-Ringel formula of the minimal right determiner still holds. As an application, we will show that the existence of minimal right determiners relates with the existence of almost split sequences in the category of representations of strongly locally finite quivers.
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu