Geodesic
On Krull-Schmidt bicategories
Theory and applications of categories, Tome 38 (2022), pp. 232-256 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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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Classification : 20J05, 18B40, 18N10, 18N25
Keywords: Bicategory, Krull--Schmidt property, 2-representation theory 
@article{TAC_2022_38_a7,
     author = {Ivo Dell'Ambrogio},
     title = {On {Krull-Schmidt} bicategories},
     journal = {Theory and applications of categories},
     pages = {232--256},
     year = {2022},
     volume = {38},
     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/