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math.CT2024
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…
math.CT2024
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…
math.CT2024
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…