# Equational Axiomatization of Algebras with Structure

arXiv: https://arxiv.org/abs/1812.02016 · HTML: https://mlsanity.com/paper/1812.02016/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2018.

## Built on by (most cited first, 2 of 2)

- [Nominal Topology for Data Languages](https://mlsanity.com/paper/2304.13337/) (2023)
- [Persistent Magnitude Homology for Quantitative Equational Theories](https://mlsanity.com/paper/2608.21479/) (2026)

## Abstract (arXiv)

This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered algebras, continuous algebras, quantitative algebras, nominal algebras, or profinite algebras. Our main contributions are a generic HSP theorem and a sound and complete equational logic, which are shown to encompass numerous flavors of equational axiomizations studied in the literature.