Geodesic
Bicategories of fractions revisited: towards small homs and canonical 2-cells
Theory and applications of categories, Tome 38 (2022), pp. 913-1014.

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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.
Publié le :
Classification : 18D05, 18E35
Keywords: bicategories of fractions, categories of fractions, localizations, orbifolds, small homs 
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     author = {Dorette Pronk and Laura Scull},
     title = {Bicategories of fractions revisited:  towards small homs and canonical 2-cells},
     journal = {Theory and applications of categories},
     pages = {913--1014},
     publisher = {mathdoc},
     volume = {38},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a23/}
}
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Dorette Pronk; Laura Scull. Bicategories of fractions revisited:  towards small homs and canonical 2-cells. Theory and applications of categories, Tome 38 (2022), pp. 913-1014. http://geodesic.mathdoc.fr/item/TAC_2022_38_a23/