A fiber product of morphisms 
and 
of schemes is a scheme 
with projection
morphisms 
to 
and 
to 
such that 
. It has the universal
property that, for every scheme 
with morphisms 
and 
satisfying the same compatibility equation, there is
a unique morphism 
inducing them.
For schemes, fiber products are precisely categorical pullbacks; "fibred product" is an alternate spelling. They are used to define base
change; for example, the base change of 
along 
is 
.
