On Krull-Schmidt bicategories

Abstract

We study the existence and uniqueness of direct sum decompositions in additive bicategories. We find a simple definition of Krull-Schmidt bicategories, for which we prove the uniqueness of decompositions into indecomposable objects as well as a characterization in terms of splitting of idempotents and properties of 2-cell endomorphism rings. Examples of Krull-Schmidt bicategories abound, with many arising from the various flavors of 2-dimensional linear representation theory.

arXiv comment21 pages, final version. Several examples added