fibre product
Let S be a scheme, and let i:X⟶S and j:Y⟶S be schemes over S. A fibre product of X and Y over S is a scheme X×SY together with morphisms
p:X×SY⟶X | ||
q:X×SY⟶Y |
such that given any scheme Z with morphisms
x:Z⟶X | ||
y:Z⟶Y |
where i∘x=j∘y, there exists a unique morphism
(x,y):Z⟶X×SY |
making the diagram