Partial morphisms and injective hulls in exact categories

Abstract: In the seminal paper where Ziegler developed the model theory of modules, he introduced, using model theoretical language, the notion of partial morphism. Later, Monari Martinez characterized this notion in module theoretical terms. In the talk, we will give a categorical characterization of partial morphisms in module categories, which will allow us to extend them to any exact category. Then, we will see how all properties of partial morphisms in module categories extend to exact categories, and we will establish their relationship with cophantom morphisms and injective objects. Finally, we will discuss how partial morphisms can be used to characterize injective hulls, and we will give a condition that implies the existence of such hulls in an exact category.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections