Remark 18.16.5. In general the functor g_! cannot be extended to categories of modules in case g is (part of) a morphism of ringed topoi. Namely, given any ring map A \to B the functor M \mapsto B \otimes _ A M has a right adjoint (restriction) but not in general a left adjoint (because its existence would imply that A \to B is flat). We will see in Section 18.19 below that it is possible to define j_! on sheaves of modules in the case of a localization of sites. We will discuss this in greater generality in Section 18.41 below.
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