Fiber product of Schemes

Definition : Let \(S\) be a scheme. An \(S\) scheme is a scheme \(X\) together with a morphism \(p:X\rightarrow S\).  A morphism of \(S\) schemes \((X,p:X\rightarrow S)\) and \((Y,q:Y\rightarrow S)\) is a morphism of schemes \(f:X\rightarrow Y\) such that \(q\circ f=p\).