Quasi-coherent sheaves in commutative and non-commutative geometry

We give a definition of quasi-coherent modules for any presheaf of sets on the categories of affine commutative and non-commutative schemes. This definition generalizes the usual one. We study the property of a quasi-coherent module to be a sheaf in various topologies. Using presheaves of groupoids, we construct an embedding of commutative geometry in non-commutative geometry.