Types of Serre subcategories of Grothendieck categories

摘要

Every Serre subcategory S of an abelian category A is assigned a unique type (m, -n), where m (resp. n) counts how many times one can form left (resp. right) adjoints starting from i and Q, where i : S - A is the inclusion and Q is the quotient functor. The main result gives a complete list of all the types of Serre subcategories of Grothendieck categories: