Milnor's theorem on Kan complexes
In mathematics, especially algebraic topology, a theorem of Milnor says that the geometric realization functor from the homotopy category of the category Kan of Kan complexes to the homotopy category of the category Top of (reasonable) topological spaces is fully faithful. The theorem in particular implies Kan and Top have the same homotopy category.
Source: Wikipedia — Milnor's theorem on Kan complexes (CC BY-SA 4.0)