Abstract:One of the goals of studying mathematical foundation is to build a solid foundation for mathematical architecture.Whether the category theory can be mathematical foundation is a vital theme for mathematical philosophers.Mathematicians use functor and isomorphism to depict the concept of mathematical structure;philosophers focus on the mathematical foundation from the perspectives of ontology,epistemology and methodology;the combination of mathematical theory and philosophical speculations makes contributions to examine category theory as mathematical foundation ultimately.

 

Key words:category theory; mathematical foundation; ontology; epistemology; methodology