On Krull-Schmidt bicategories
Category Theory
2022-01-31 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.2111.06965,
title = {On Krull-Schmidt bicategories},
author = {Ivo Dell'Ambrogio},
journal= {arXiv preprint arXiv:2111.06965},
year = {2022}
}
Comments
21 pages, final version. Several examples added