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