  The homotopy theory of higher categorical structures has become a relevant
part of the machinery of algebraic topology and algebraic K-theory, and this
paper contains contributions to the study of the relationship between
B\'enabou's bicategories and the homotopy types of their classifying spaces.
Mainly, we state and prove an extension of Quillen's Theorem B by showing,
under reasonable necessary conditions, a bicategory-theoretical interpretation
of the homotopy-fibre product of the continuous maps induced on classifying
spaces by a diagram of bicategories $\mathcal{A}\to\mathcal{B}\leftarrow
\mathcal{A}'$. Applications are given for the study of homotopy pullbacks of
monoidal categories and of crossed modules.
