The main aim of this note is to show that, in the regular context, every matrix property in the sense of [13] either implies the Mal'tsev property, or is implied by the majority property. When the regular category C is arithmetical, i.e., both Mal'tsev and a majority category, then we show that C satisfies every non-trivial matrix property.
Keywords: Arithmetical category, Mal'tsev category, majority category, matrix property, Mal'tsev condition.
2020 MSC: 18E13, 08B05, 18E08, 08A05, 06-08
Theory and Applications of Categories, Vol. 44, 2025, No. 23, pp 664-675.
Published 2025-08-05.
TAC Home