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

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.

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