How can we understand an abelian category?

Abstract: 

Abelian categories are a generalisation of a module categories and play an important role in areas such as algebraic topology and algebraic geometry. A well-known result of Morita states that any abelian category with a progenerator is equivalent to a module category. However, not all abelian categories are modules categories.

In this talk we will introduce the notion of a quotient of an abelian category and present a Morita-type result, giving necessary and sufficient conditions for an abelian category to be equivalent to a quotient of the category of graded right modules over some graded algebra.