Coextension of scalars (${\mathrm{Hom}}_R(A,M)$)

For a ring homomorphism $R\to A$ and a left $R$-module $M$, the left $A$-action on ${\mathrm{Hom}}_R(A,M)$ is $(a\cdot h)(b)=h(ba)$. This construction is right adjoint to restriction of scalars.