Functoriality in Sheaves of Modules and Quasi-Coherent/Coherent Sheaves

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We talk about exact sequence of modules, localisation being an exact functor, and end with Description of Quasicoherent and Coherent sheaves
Ref: Daniel Perrin, Algebraic Geometry
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It is not obvious that the two definitions of quasi-coherent module are equivalent. Do you have a specific reference for this, thanks.

brucegreetham