I am not sure this is standard terminology but the notes I am using has a mapping defined as follows. In particular I need help with how to write out the definition in some related exercises.
Let $R$ be a commutative ring with identity. Let $M,N,P$ be $R$ modules and let $\theta : Hom_A (M,N) \otimes_R P \rightarrow Hom_A (M,N \otimes_R P)$ be the canonical mapping.
Is the canonical mapping theta given by $(f,y) \rightarrow (x \rightarrow (x \rightarrow f(x \otimes y))$ for $f \in Hom_A (M,N)$ and $ y \in P$?