# II.1.15

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• In particular, the zero and gluing sheaf axioms for Hom$(F|_U,G|_U)$ (here the underline means sheaf Hom) only require that G be a sheaf. For example, for the zero axiom, if a morphism restricts to 0 on some open cover means that the original morhpism maps elements to other elements that restricts to 0 in the groups of G, as G is a sheaf, the morphism must be mapping everything to 0.