Geodesic
Some insights on bicategories of fractions: representations and compositions of 2-morphisms
Theory and applications of categories, Tome 31 (2016), pp. 257-329

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In this paper we investigate the construction of bicategories of fractions originally described by D.~Pronk: given any bicategory $C$ together with a suitable class of morphisms $W$, one can construct a bicategory $C[W^{-1}]$, where all the morphisms of $W$ are turned into internal equivalences, and that is universal with respect to this property. Most of the descriptions leading to this construction were long and heavily based on the axiom of choice. In this paper we considerably simplify the description of the equivalence relation on 2-morphisms and the constructions of associators, vertical and horizontal compositions in $C[W^{-1}]$, thus proving that the axiom of choice is not needed under certain conditions. The simplified description of associators and compositions will also play a crucial role in two forthcoming papers about pseudofunctors and equivalences between bicategories of fractions.

Publié le :
Classification : 18A05, 18A30, 22A22
Keywords: bicategories of fractions, bicalculus of fractions, pseudofunctors 
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     title = {Some insights on bicategories of fractions: representations and
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Matteo Tommasini. Some insights on bicategories of fractions: representations and
compositions of 2-morphisms. Theory and applications of categories, Tome 31 (2016), pp. 257-329. http://geodesic.mathdoc.fr/item/TAC_2016_31_a9/