fibre product

Let $S$ be a scheme, and let $i:X\\longrightarrow S$ and $j:Y\\longrightarrow S$ be schemes over $S$ . A fibre product of $X$ and $Y$ over $S$ is a scheme $X\\times_{S}Y$ together with morphisms

	$\\displaystyle p:X\\times_{S}Y\\longrightarrow X$
	$\\displaystyle q:X\\times_{S}Y\\longrightarrow Y$

such that given any scheme $Z$ with morphisms

	$\\displaystyle x:Z\\longrightarrow X$
	$\\displaystyle y:Z\\longrightarrow Y$

where $i\\circ x=j\\circ y$ , there exists a unique morphism

(x,y):Z\\longrightarrow X\\times_{S}Y

making the diagram