Category Theory is the mathematical theory of structure-respecting transformations. A category consists of arrows (or morphisms) between objects. For example, we can form a category by taking partially ordered sets as the objects and order-respecting mappings as the arrows. Using general category-theoretical notions, we can then determine the meaning of such concepts as the product of two partially ordered sets. Such general notions are typically defined by universal properties, which determine the result uniquely (up to isomorphism).

For further online information, see: A Gentle Introduction to Category Theory - the calculational approach, by Maarten Fokkinga, http://www.cs.utwente.nl/~fokkinga/mmf92b.ps