Corollary

Let M and $M'$ be isotypical A-modules of type S. The mapping $u\mapsto$ Hom(1$_S, u$) from Hom$_A(M,M')$ to Hom$_D$(Hom$_A(S,M)$, Hom$_A(S,M')$) is a group isomorphism. When M is equal to $M'$, it is a ring isomorphism from End$_A(M)$ to End$_D$(Hom$_A(S,M)$).

Because of the commutativity of diagram (I) of VIII, p. 59, this corollary follows from Theorem 3, applied to the canonical descriptions of M and $M'$.