A D18: Map $f : X \to Y$ is an identity map on $X$ if and only if \begin{equation} \forall \, x \in X : f(x) = x \end{equation}

A D18: Map $f : X \to Y$ is an identity map on $X$ if and only if $x$ is a D551: Fixed point of $f$ for every $x \in X$.