Let $G$ be a D265: Monoid such that

(i)	$I_G$ is an D39: Identity element in $G$

Let $f : X \to G$ be a D18: Map.
The support of $f$ with respect to $G$ is the D11: Set \begin{equation} \{ x \in X : f(x) \neq I_G \} \end{equation}