Given a functor T:C→D carrying a class of morphisms S⊂C into a
class S′⊂D, we give sufficient conditions in order that T induces an
equivalence on the localised categories. These conditions are in the spirit of
Quillen's theorem A. We give some applications in algebaic and birational
geometry.Comment: File mistake in Version 2 To appear in Homology, Homotopy and
Application