  This text develops a homotopy theory of 2-categories analogous to
Grothendieck's homotopy theory of categories developed in "Pursuing Stacks". We
define the notion of "basic localizer of 2-Cat", 2-categorical generalization
of Grothendieck's notion of basic localizer, and we show that the homotopy
theories of $Cat$ and 2-$Cat$ are equivalent in a remarkably strong sense:
there is an isomorphism, compatible with localization, between the ordered
classes of basic localizers of $Cat$ and 2-$Cat$. It follows that weak homotopy
equivalences in 2-$Cat$ can be characterised in an internal way, without
mentioning topological spaces or simplicial sets.

Algebraic Topology