  Like categories, small 2-categories have well-understood classifying spaces.
In this paper, we deal with homotopy types represented by 2-diagrams of
2-categories. Our results extend to homotopy colimits of 2-functors lower
categorical analogues that have been classically used in algebraic topology and
algebraic K-theory, such as the Homotopy Invariance Theorem (by Bousfield and
Kan), the Homotopy Colimit Theorem (Thomason), Theorems A and B (Quillen), or
the Homotopy Cofinality Theorem (Hirschhorn).
