Set of Homomorphisms to Abelian Group is Subgroup of All Mappings

Theorem
Let $$\left({S, \circ}\right)$$ be an algebraic structure.

Let $$\left({T, \oplus}\right)$$ be a commutative semigroup.

Let $$\left({T^S, \oplus}\right)$$ be the algebraic structure on $T^S$ induced by $\oplus$

Then the set of all homomorphisms from $$\left({S, \circ}\right)$$ into $$\left({T, \oplus}\right)$$ is a subgroup of $$\left({T^S, \oplus}\right)$$.