  We study the interaction between the notions of filteredness, fractions and
fibrations in the theory of bicategories, generalizing classical results for
categories. We give an explicit formula for filtered pseudo-colimits of
categories indexed by a bicategory, and we use it to compute the hom-categories
of a bicategory of fractions. As a consequence, we show that the canonical
pseudo-functor into a bicategory of fractions is exact.
