Mappings to Algebraic Structure form Similar Algebraic Structure

Theorem
Let $X$ be a nonempty set.

Let $G$ be a magma with respect to the binary operations $\circ_1, \ldots, \circ_n$ on $G$.

Let $G^X$ be the set of all mappings from $X$ to $G$.

Denote also by $\circ_1, \ldots, \circ_n$ the binary operations defined on $G^X$ by pointwise addition.

Also see

 * Mappings to R-Algebraic Structure form Similar R-Algebraic Structure