A limit lifting theorem for fibrations between bicategories

Abstract

A standard result from the theory of Grothendieck fibrations states that if $p : E \to B$ is a fibration, then $E$ has limits of shape $\mathcal{J}$ if $B$ has limits of shape $\mathcal{J}$ the fibers of $\mathcal{E}$ have limits of shape $\mathcal{J}$, and the reindexing functors preserve these limits. Such a result is a basic tool when computing limits in a category known to be the total category of a fibration, for example, one that is defined using the Grothendieck construction. This paper states and proves a generalization of this theorem for fibrations between bicategories.