Morphism on Proj induced by a graded ring homomorphism
= Morphism on Proj induced by a graded ring homomorphism
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A graded homomorphism $S\to T$ induces a morphism to $\operatorname{Proj}S$ on the open subset of $\operatorname{Proj}T$ where the inverse image of a prime does not contain $S_+$. On $D_+(\varphi(f))$ it is induced by $(S_f)_0\to(T_{\varphi(f)})_0$.