The Stacks project

Exercise 110.65.5 (Monomorphisms). Let $f : X \to Y$ be a monomorphism in the category of schemes: for any pair of morphisms $a, b : T \to X$ of schemes if $f \circ a = f \circ b$, then $a = b$. Show that $f$ is injective on points. Does you argument say anything else?

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