Thus we only need to prove that if gf is closed, so is g , which can be verified easily. Y is a morphism. Thus we are reduced to prove that the hypotheses implies f is closed, which is obvious. Then p is universally closed. Any special morphism is universally closed.
Y are two morphisms in a site C .
Y' is universally injective. Then f is universally injective. Since f ' is universally injective, so is f 1 '. Since h is surjective, so is h 1 . This shows that f is universally injective.