Homotopies in grothendieck fibrations

We define a natural 2-categorical structure on the base category of a large class of Grothendieck fibrations. Given any model category C, we apply this construction to a fibration whose fibers are the homotopy categories of the slice categories C/A, and we show that in the case C = Top, our construction applied to this fibration recovers the usual 2-category of spaces.