  This work contributes to clarifying several relationships between certain
higher categorical structures and the homotopy type of their classifying
spaces. Bicategories (in particular monoidal categories) have well understood
simple geometric realizations, and we here deal with homotopy types represented
by lax diagrams of bicategories, that is, lax functors to the tricategory of
bicategories. In this paper, it is proven that, when a certain bicategorical
Grothendieck construction is performed on a lax diagram of bicategories, then
the classifying space of the resulting bicategory can be thought of as the
homotopy colimit of the classifying spaces of the bicategories that arise from
the initial input data given by the lax diagram. This result is applied to
produce bicategories whose classifying space has a double loop space with the
same homotopy type, up to group completion, as the underlying category of any
given (non-necessarily strict) braided monoidal category. Specifically, it is
proven that these double delooping spaces, for categories enriched with a
braided monoidal structure, can be explicitly realized by means of certain
genuine simplicial sets characteristically associated to any braided monoidal
categories, which we refer to as their (Street's) geometric nerves.
