The Importance of Developing a Foundation for Naive Category Theory
Abstract
Recently Feferman (Rev. Symb. Logic 6: 6-15, 2013) has outlined a program for the development of a foundation for naive category theory. While Ernst (ibid. 8: 306-327, 2015) has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a 'cookbook recipe' is used for constructing categories, and it is explicitly shown with a formalized argument that this 'foundationless' naive category theory therefore contains a paradox similar to the Russell paradox of naive set theory.
Keywords
Cite
@article{arxiv.1509.08814,
title = {The Importance of Developing a Foundation for Naive Category Theory},
author = {Marcoen J. T. F. Cabbolet},
journal= {arXiv preprint arXiv:1509.08814},
year = {2015}
}
Comments
Proof that Category Theory in its current state of development is inconsistent; 4 pages; to appear in Thought