Grothendieck's homotopy hypothesis

Axiom M (Grothendieck’s homotopy hypothesis). The morphisms inverted by the functor \(\Pi _{\infty }\colon \Top \to \An \) are precisely the weak homotopy equivalences. Moreover, \(\Pi _{\infty }\) exhibits \(\An \) as a localization of \(\Top \) at the weak homotopy equivalences, that is, it induces an equivalence of \(\infty \)-categories \[ \Top [\{\text {weak homotopy equivalences}\}^{-1}] \iso \An . \]