The fiber product of schemes always exists. That is, for any schemes "X" and "Z" with morphisms to a scheme "Y", the fiber product "X"×"Y""Z" (in the sense of category theory) exists in the category of schemes. If "X" and "Z" are schemes over a field "k", their fiber product over Spec("k") may be called the product "X" × "Z" in the category of "k"-schemes. For example, the product of affine spaces A"m" and A"n" over "k" is affine space A"m"+"n" over "k".