Some insights on bicategories of fractions – I

Reference : Some insights on bicategories of fractions – I


	Document type :	E-prints/Working papers : Already available on another site
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/19072

Title :	Some insights on bicategories of fractions – I
Language :	English
Author, co-author :	Tommasini, Matteo [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2014
Number of pages :	48
Peer reviewed :	No
Keywords :	[en] bicategories of fractions ; bicalculus of fractions ; pseudofunctors
Abstract :	[en] 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 such a construction were long and heavily based on the axiom of choice. In this paper we simplify considerably the constructions of associators, vertical and horizontal compositions in a bicategory of fractions, thus proving that the axiom of choice is not needed under certain conditions. The simplified description of associators and 2-compositions will also play a crucial role in the next papers of this series.
Funders :	Fonds National de la Recherche - FnR
Permalink :	http://hdl.handle.net/10993/19072
source URL :	http://arxiv.org/abs/1410.3990

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