Year: 2015
Type: preprint
Abstract: We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by categories. Since there are infinitary constructions in category theory, it is shown that category theory is strictly more powerful than Turing machines. In particular, categories can solve the Halting Problem for Turing machines. We also show that categories can solve any problem in the arithmetic hierarchy.
Source: arXiv (Cornell University)
Author: Yanofsky, Noson S.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2253637581