Weak fiber products in a bicategory of fractions

TL;DR

This paper investigates conditions under which weak fiber products exist in a localized bicategory of fractions, providing a precise characterization within the framework of bicategories and calculus of fractions.

Contribution

It establishes necessary and sufficient conditions for the existence of weak fiber products in bicategories of fractions, advancing the understanding of their structure.

Findings

Identifies conditions for weak fiber products in bicategories of fractions

Provides a characterization of existence criteria

Enhances the theory of bicategory localizations

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.