A limit lifting theorem for fibrations between bicategories

A standard result from the theory of Grothendieck fibrations states that if p : E → B is a fibration, then E has limits of shape J if B has limits of shape J the fibers of E have limits of shape 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.