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Dec 14, 2011 at 22:16 comment added Martin Brandenburg This application comes also into life in the great paper "Descent Theory for Schemes" by Bachuki Mesablishvili. There the author generalizes Grothendieck's descent theory from fpqc morphisms to pure morphisms, which are morphisms which are schematically dense and stay so after arbitrary base change. Very recommended! The author also uses general theorems of factorization systems in categories - although in this case can be done also in a ad hoc manner without any additional effort. See also my answer here: mathoverflow.net/questions/48047/…
Dec 14, 2011 at 22:04 history answered Finn Lawler CC BY-SA 3.0