Weak fiber products in a bicategory of fractions

Abstract: We fix any pair $(\mathbf{\mathscr{C}},\mathbf{W})$ consisting of a bicategory and a class of morphisms in it, admitting a bicalculus of fractions, i.e. a "localization" of $\mathbf{\mathscr{C}}$ with respect to the class $\mathbf{W}$. In the resulting bicategory of fractions, we identify necessary and sufficient conditions for the existence of weak fiber products.