Category theory is a unifying theory of mathematics that was initially developed in the second half of the 20th century. In this respect it is an alternative and complement to set theory. A key theme from the “categorical” point of view is that mathematics requires not only certain kinds of objects (Lie groups, Banach spaces, etc.) but also mappings between them that preserve their structure.
In particular, this clarifies exactly what it means for mathematical objects to be considered to be the same.
— Wikipedia on Unifying theories in mathematics
2010.01.11 Thursday ACHK