If $X' \subseteq X$ then we may define an inclusion map $\iota : X' \to X$ where $\iota(x) = x$. One use of $\iota$ is that we can express the restriction of some $f : X \to Y$ to $X'$ as $f|_{X'} = f \circ \iota$.
This can be useful when representing function restrictions in commutative diagrams. But how about restricting binary relations in commutative diagrams?
The restriction of some binary relation $R \subseteq X \times X$ to $X'$ can be rather neatly expressed as $R \cap (X')^2$, but I would like to express it as the composite relation $R \circ I$, where $I = \{(x, x)\ |\ x \in X'\}$.
So my question is, does $I$ have a standard name or notation? Maybe something like $1_{X'}$...