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Bicategories of fractions revisited: towards small homs and canonical 2-cells

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Dorette Pronk and Laura Scull

This paper addresses two issues in dealing with bicategories of fractions. The first is to introduce a set of conditions on a class of arrows in a bicategory which is weaker than the one given in [5] but still allows a bicalculus of fractions. These conditions allow us to invert a smaller collection of arrows so that in some cases we may obtain a bicategory of fractions with small hom-categories. We adapt the construction of the bicategory of fractions to work with the weaker conditions. The second issue is the difficulty in dealing with 2-cells, which are defined by equivalence classes. We discuss conditions under which there are canonical representatives for 2-cells, and how pasting of 2-cells can be simplified in the presence of certain pseudo pullbacks. We also discuss how both of these improvements apply in the category of orbispaces.

Keywords:
bicategories of fractions, categories of fractions, localizations, orbifolds, small homs

2020 MSC:
18D05, 18E35

*Theory and Applications of Categories,*
Vol. 38, 2022,
No. 24, pp 913-1014.

Published 2022-08-18.

http://www.tac.mta.ca/tac/volumes/38/24/38-24.pdf

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