Discrete equational theories
Category Theory
2025-01-14 v4
Abstract
We introduce discrete equational theories where operations are induced by those having discrete arities. We characterize the corresponding monads as monads preserving surjections. Using it, we prove Birkhoff type theorems for categories of algebras of discrete theories. This extends known results from metric spaces to general symmetric monoidal closed categories.
Cite
@article{arxiv.2204.02590,
title = {Discrete equational theories},
author = {Jiří Rosický},
journal= {arXiv preprint arXiv:2204.02590},
year = {2025}
}
Comments
an updated and corrected version, 17 pages