nLab graph morphism

Let $C$ be a category admitting finite fibred products and $f : X \to Y$ be a morphism over some base $S$. The graph morphism of $f$ is the morphism

$$\Gamma_f \colon X \to X \times_S Y$$

induced by $\mathbf{1}_X : X \to X$ and $f : X \to Y$.

The image of the graph morphism of $f$ is called the graph of $f$.