On Krull-Schmidt bicategories

Ivo Dell'Ambrogio

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.

Keywords: Bicategory, Krull--Schmidt property, 2-representation theory

2020 MSC: 20J05, 18B40, 18N10, 18N25

Theory and Applications of Categories, Vol. 38, 2022, No. 8, pp 232-256.

Published 2022-01-27.


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