When a matrix condition implies the Mal'tsev property

Michael Hoefnagel; Pierre-Alain Jacqmin

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arXiv · 2208.09516

When a matrix condition implies the Mal'tsev property

Michael Hoefnagel·Pierre-Alain Jacqmin

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Abstract

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 general, they can only be stated for regular categories. We study when such a matrix condition implies the Mal'tsev property. Our main results assert that, for both types of matrices, this implication is equivalent to the corresponding implication restricted to the context of varieties of universal algebras.

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Michael Hoefnagel, Pierre-Alain Jacqmin. 2022-08-19. When a matrix condition implies the Mal'tsev property. https://arxiv.org/abs/2208.09516

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