= Graph morphism of schemes
{title2=$\Gamma_f=(\operatorname{id}_X,f):X\to X\times_ZY$}
For <morphisms of schemes> $f:X\to Y$ and $g:Y\to Z$, the graph is the displayed map. It is the pullback of the <diagonal morphism> $Y\to Y\times_ZY$ along $(f\circ p_X,p_Y)$. Thus a <separated morphism> $g$ makes $\Gamma_f$ a <closed immersion>. If also $g\circ f$ is a <closed immersion>, the projection $X\times_ZY\to Y$ is a <closed immersion> by <base change of a morphism of schemes>, and its composite with $\Gamma_f$ proves that $f$ is a <closed immersion>.
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