Example 56.3.2. Let $R$ be a ring. Let $A$ and $B$ be $R$-algebras. Let $K$ be a $A \otimes _ R B$-module. Then we can consider the functor
This functor is $R$-linear, right exact, commutes with arbitrary direct sums, commutes with all colimits, has a right adjoint (Lemma 56.3.1).