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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

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Projectives in the category of quasi coherent sheaves Qch(X)

X is a non singular projective variety over an infinite field k. How to prove there are no projectives with a surjective map to the structure sheaf O_X in Qch(X) and Coh(X). Coh(X) is the category of …