Geodesic
Free globularly generated double categories I
Theory and applications of categories, Tome 34 (2019), pp. 1343-1385

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This is the first part of a two paper series studying free globularly generated double categories. In this first installment we introduce the free globularly generated double category construction. The free globularly generated double category construction canonically associates to every bicategory together with a possible category of vertical morphisms, a double category fixing this set of initial data in a free and minimal way. We use the free globularly generated double category to study length, free products, and problems of internalization. We use the free globularly generated double category construction to provide formal functorial extensions of the Haagerup standard form construction and the Connes fusion operation to inclusions of factors of not-necessarily finite Jones index.

Publié le :
Classification : 18B30, 18D05, 18F15
Keywords: Category, double category, bicategory, von Neumann algebra, representation, fusion, tensor category, length 
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     author = {Juan Orendain},
     title = {Free globularly generated double categories {I}},
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     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a41/}
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Juan Orendain. Free globularly generated double categories I. Theory and applications of categories, Tome 34 (2019), pp. 1343-1385. http://geodesic.mathdoc.fr/item/TAC_2019_34_a41/