Coproduct

A dual notion to the Product.
Let and be Objects of a Category .
Their coproduct consists of maps and
such that for any and
there is a unique
making the following a Commutative Diagram

If is Locally Small we can have a Functor defined by

If is Representable, with Representation
then its Universal Element is some
where and
and this is exactly the coproduct.

In the Category of Sets, the coproduct is the disjoint union

together with maps and .