Dual
For every construction in Category Theory, the opposite construction can be made by reversing the morphisms. This opposite construction is usually named by prefixing the original name with "co-". 1
An example of dual categories can be seen in the product and sum operations from Set Theory. In each of the product and sum operations, you can consider "imposter" sums and "imposter" products which contain additional information which can be removed with a morphism. 2
Specifically, you can always create a new
imposter sum with a trivial function that goes from
A + B -> A + B + X and you can
always create a new imposter product that goes from
A x B x X -> A x B. You can see by
looking at the formulas how the extra information
X is on different sides of the
function. 2
Anything that has this kind of relationship is said to be dual to one another. The concepts of product and sum are dual and it's why sums are known as converse product or coproduct. 2