  We define a tensor product of linear sites, and a resulting tensor product of
Grothendieck categories based upon their representations as categories of
linear sheaves. We show that our tensor product is a special case of the tensor
product of locally presentable linear categories, and that the tensor product
of locally coherent Grothendieck categories is locally coherent if and only if
the Deligne tensor product of their abelian categories of finitely presented
objects exists. We describe the tensor product of non-commutative projective
schemes in terms of Z-algebras, and show that for projective schemes our tensor
product corresponds to the usual product scheme.
