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.Comment: Published in Theory and Applications of Categorie