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Exponentiability Of Perfect Maps: Four Approaches - Niefield (2002) (Correct)
....by Richter and Tholen, is a general categorical proof that pullback along a perfect morphism preserves quotient maps. The setting there is a finitely complete category with a proper pullback stable factorization system. Though constructive itself, one then uses Freyd s Adjoint Functor Theorem [Fr] to obtain exponentiability of perfect maps in Top. Here we present two additional proofs. One is implicit in the literature but uses internal locales in the category of sheaves on a topological space and a theorem from [N3] for which it is necessary to assume that the codomain of the perfect map ....
P. Freyd, Abelain Categories, Harper & Row, New York, 1964.
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