In the situation $(_RA,_RC_S)$, prove that if $A$ is $R$-projective and $C$ is $S$-injective then $\operatorname{Hom}_R(A,C)$ is $S$-injective.
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2026-03-26 22:18:05.1774563485
Prove that if $A$ is $R$-projective and $C$ is $S$-injective then $\operatorname{Hom}_R(A,C)$ is $S$-injective
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This is a consequence of Tensor-Hom adjunction. In particular it suffices to assume that $A$ is flat, which is slightly weaker than projective.