Ivo Dell’Ambrogio - Université de Lille

On Krull-Schmidt bicategories

ABSTRACT: The Krull-Schmidt property for additive categories is a basic tool of representation theory. After reviewing the classical definitions and results, I will explain how the latter can be adapted to the study of direct sum decompositions inside additive bicategories. The resulting theory is simpler and easier to apply than one may expect. I will discuss several examples, in particular from 2-representation theory.