5 papers · 1 filter
Partial algebras and implications of (weak) matrix properties
Michael Hoefnagel, Pierre-Alain Jacqmin
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algo…
A note on the atomicity of arithmeticity
Michael Hoefnagel, Pierre-Alain Jacqmin
The main aim of this note is to show that, in the regular context, every matrix property in the sense of Z. Janelidze either implies the Mal'tsev property, or is implied by the maj…
Categorical aspects of congruence distributivity
Michael Hoefnagel, Diana Rodelo
We study a categorical condition on relations, which is a categorical formulation of Jónsson's characterisation of congruence distributive varieties. Categories satisfying these co…
When a matrix condition implies the Mal'tsev property
Michael Hoefnagel, Pierre-Alain Jacqmin
Matrix conditions extend linear Mal'tsev conditions from Universal Algebra to exactness properties in Category Theory. Some can be stated in the finitely complete context while, in…
Matrix taxonomy and Bourn localization
Michael Hoefnagel, Pierre-Alain Jacqmin
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `m…