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

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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 
@article{TAC_2022_38_a23,
     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/}
}
TY  - JOUR
AU  - Dorette Pronk
AU  - Laura Scull
TI  - Bicategories of fractions revisited:  towards small homs and canonical 2-cells
JO  - Theory and applications of categories
PY  - 2022
SP  - 913
EP  - 1014
VL  - 38
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2022_38_a23/
LA  - en
ID  - TAC_2022_38_a23
ER  - 
%0 Journal Article
%A Dorette Pronk
%A Laura Scull
%T Bicategories of fractions revisited:  towards small homs and canonical 2-cells
%J Theory and applications of categories
%D 2022
%P 913-1014
%V 38
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2022_38_a23/
%G en
%F TAC_2022_38_a23
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/