In Pursuing stacks, Grothendieck defines basic localizors as classes of weak equivalences in the category of small categories satisfying good descent properties (closely related to Quillen's theorem A). For example, the usual weak equivalences (defined by the nerve functor) form a basic localizor. More generally, every cohomological theory on small categories defines canonically a basic localizor. In this paper, we give a proof of Grothendieck's conjecture that states that the class of usual weak equivalences is the smallest basic localizor. This gives an elementary and axiomatic way to define the classical homotopy theory of CW-complexes.