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arXiv · 2111.06965

On Krull-Schmidt bicategories

Ivo Dell'Ambrogio
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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.

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Ivo Dell'Ambrogio. 2021-11-12. On Krull-Schmidt bicategories. https://arxiv.org/abs/2111.06965

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