Year: 2026
Type: preprint
Abstract: In this paper we prove that the Mal'tsev condition expressing the existence of group operations is not equivalent to a categorical property. More precisely, using pseudo-invertible idempotents, we construct two varieties $\mathcal{V}$ and $\mathcal{V}(f)$ which are equivalent as categories, and such that $\mathcal{V}$ admits group operations, whereas $\mathcal{V}(f)$ does not. We also show that those Mal'tsev conditions which are equivalent to a categorical property have a trivial spectrum.
Source: arXiv (Cornell University)
Author: Stewart, Carlyle
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223682100