A fiber product of morphisms 
and 
of schemes is a scheme
with projection morphisms
to 
and 
such that the resulting square is a commutative
diagram and has the universal property
that, for every scheme 
with compatible morphisms 
and 
, there is a unique induced morphism
.
Fiber products are also called pullbacks or fibred products. They are used to define base change; for example,
the base change of 
along 
is 
.
