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 $\mathbf{C}$, we apply this construction to a fibration whose fibers are the homotopy categories of the slice categories $\mathbf{C}\mathrm{/}A$, and we show that in the case $\mathbf{C}=\mathbf{T}\mathbf{o}\mathbf{p}$, our construction applied to this fibration recovers the usual 2-category of spaces.