# Only up to isomorphism? Category Theory and the Foundations of Mathematics

- Publication Year:
- 2010

## Explore PlumX Metrics

What are PlumX Metrics? How can they help tell the story about this research? How can I use them?

Learn more- Repository URL:
- http://philsci-archive.pitt.edu/id/eprint/5392

- Author(s):

##### preprint description

Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory. Focusing on a categorical theory of sets, we argue that a strong case can be made for its logical and conceptual autonomy. Its justificatory autonomy turns on whether the objects of a foundation for mathematics should be specified only up to isomorphism, as is customary in other branches of contemporary mathematics. If such a specification suffices, then a category-theoretical approach will be highly appropriate. But if sets have a richer 'nature' than is preserved under isomorphism, then such an approach will be inadequate.