Partial algebras and implications of (weak) matrix properties

Michael Hoefnagel; Pierre-Alain Jacqmin

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arXiv · 2404.14166

Partial algebras and implications of (weak) matrix properties

Michael Hoefnagel·Pierre-Alain Jacqmin

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Abstract

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 algorithm has been developed to determine implications $M\Rightarrow N$ between them. We show here that this algorithm reduces to construct a partial term corresponding to $N$ from a partial term corresponding to $M$. Moreover, we prove that this is further equivalent to the corresponding implication between the weak versions of these properties, i.e., the one where only strong monomorphisms are considered instead of all monomorphisms.

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Michael Hoefnagel, Pierre-Alain Jacqmin. 2024-04-22. Partial algebras and implications of (weak) matrix properties. https://arxiv.org/abs/2404.14166

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