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Free globularly generated double categories I

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Juan Orendain

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.

Keywords:
Category, double category, bicategory, von Neumann algebra,
representation, fusion, tensor category, length

2010 MSC:
18B30,18D05,18F15

*Theory and Applications of Categories,*
Vol. 34, 2019,
No. 42, pp 1343-1385.

Published 2019-12-06.

http://www.tac.mta.ca/tac/volumes/34/42/34-42.pdf

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