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Lifting bicategories into double categories: The globularily generated condition

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Juan Orendain

This is the first part of a series of papers studying the problem of
existence of double categories for which horizontal bicategory and object
category are given. We refer to this problem as the problem of existence
of internalizations for decorated bicategories. Motivated by this we
introduce the condition of a double category being globularily generated.
We prove that the problem of existence of internalizations for a decorated
bicategory admits a solution if and only if it admits a globularily
generated solution, and we prove that the condition of a double category
being globularily generated is precisely the condition of a solution to
the problem of existence of internalizations for a decorated bicategory
being minimal in a sense which we will make precise. The study of the
condition of a double category being globularily generated will thus be
pivotal in our study of the problem of existence of internalizations.

Keywords:
categories,double categories, bicateogries, von Neumann
algebras,cobordisms,algebras, bimodules

2010 MSC:
18B30,18D05,18F15

*Theory and Applications of Categories,*
Vol. 34, 2019,
No. 4, pp 80-108.

Published 2019-02-22.

http://www.tac.mta.ca/tac/volumes/34/4/34-04.pdf

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