Let $f: (X, O_X) \rightarrow (Y, O_Y)$ be a scheme morphism, $F$ - module over $O_X$, $G$ - module over $O_Y$. How to prove, that $$ Hom_{O_X}(f^*G, F) = Hom_{O_Y}(G, f_* F). $$ Please give the most detailed proof.
2026-03-27 22:57:35.1774652255
Functors $f^*$ and $f_*$ on the category of sheafs of modules (Hartshorne)
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