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},
     language = {en},
     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/