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 bicat
egory of fractions, we identify necessary and sufficient conditions for the existence of weak fiber products.
We fix any bicategory $mathscr{A}$ together with a class of morphisms $mathbf{W}_{mathscr{A}}$, such that there is a bicategory of fractions $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$. Given another such pair $(mathscr{B},mathbf{W}_{mathscr{B}})$ and
any pseudofunctor $mathcal{F}:mathscr{A}rightarrowmathscr{B}$, we find necessary and sufficient conditions in order to have an induced equivalence of bicategories from $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$ to $mathscr{B}[mathbf{W}_{mathscr{B}}^{-1}]$. In particular, this gives necessary and sufficient conditions in order to have an equivalence from any bicategory of fractions $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$ to any given bicategory $mathscr{B}$.
We fix any bicategory $mathscr{A}$ together with a class of morphisms $mathbf{W}_{mathscr{A}}$, such that there is a bicategory of fractions $mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]$. Given another such pair $(mathscr{B},mathbf{W}_{mathscr{B}})$ and
any pseudofunctor $mathcal{F}:mathscr{A}rightarrowmathscr{B}$, we find necessary and sufficient conditions in order to have an induced pseudofunctor $mathcal{G}:mathscr{A}[mathbf{W}_{mathscr{A}}^{-1}]rightarrow mathscr{B}[mathbf{W}_{mathscr{B}}^{-1}]$. Moreover, we give a simple description of $mathcal{G}$ in the case when the class $mathbf{W}_{mathscr{B}}$ is right saturated.
