Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 664-675 |
| Number of pages | 12 |
| Journal | Theory and Applications of Categories |
| Volume | 44 |
| Issue number | 23 |
| Publication status | Published - 2025 |
Keywords
- Arithmetical category
- Mal’tsev category
- Mal’tsev condition
- majority category
- matrix property
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