The categorical notion which is dual to product. The coproduct of a family 
of objects of a category is an object 
, together with a family of morphisms 
such that for
every object 
and every family of morphisms 
there is an unique morphism 
such that
 |
for all 
.
The coproduct is unique up to isomorphisms.
In the category of sets, the coproduct is the disjoint union 
, and 
is the inclusion. In the category of Abelian groups,
the coproduct is the group direct sum 
, and 
is the injection of the 
th summand. In the category of groups, the coproduct is the
free product of groups.
