Indicator function operator

Let $X$ be a D17: Finite set such that
 (i) $\mathcal{P}(X)$ is the D80: Power set of $X$ (ii) $\{ 0, 1 \}^X$ is the D68: Set of maps from $X$ to $\{ 0, 1 \}$
The indicator function operator on $\mathcal{P}(X)$ is the D18: Map $$\mathcal{P}(X) \to \{ 0, 1 \}^X, \quad E \mapsto I_E$$