2014/01/01 by Matteo Tommasini, Tommasini, Matteo
Mathematics · #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1410.3990
openalex publication_date 2014/01/01 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
In this paper we investigate the construction of bicategories of fractions\noriginally described by D. Pronk: given any bicategory \C together\nwith a suitable class of morphisms \W, one can construct a bicategory\n\C[\W-1], where all the morphisms of \W are\nturned into internal equivalences, and that is universal with respect to this\nproperty. Most of the descriptions leading to this construction were long and\nheavily based on the axiom of choice. In this paper we considerably simplify\nthe description of the equivalence relation on 2-morphisms and the\nconstructions of associators, vertical and horizontal compositions in\n\C[\W-1], thus proving that the axiom of choice is not\nneeded under certain conditions. The simplified description of associators and\ncompositions will also play a crucial role in two forthcoming papers about\npseudofunctors and equivalences between bicategories of fractions.\n