Geodesic
On Krull-Schmidt bicategories
Theory and applications of categories, Tome 38 (2022), pp. 232-256.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Publié le :
Classification : 20J05, 18B40, 18N10, 18N25
Keywords: Bicategory, Krull--Schmidt property, 2-representation theory 
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     author = {Ivo Dell'Ambrogio},
     title = {On {Krull-Schmidt} bicategories},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a7/}
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Ivo Dell'Ambrogio. On Krull-Schmidt bicategories. Theory and applications of categories, Tome 38 (2022), pp. 232-256. http://geodesic.mathdoc.fr/item/TAC_2022_38_a7/