Matrix taxonomy and Bourn localization

Michael Hoefnagel; Pierre-Alain Jacqmin

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arXiv · 2208.09509

Matrix taxonomy and Bourn localization

Michael Hoefnagel·Pierre-Alain Jacqmin

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Abstract

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 `matrix properties'. In this paper we extend this algorithm to include matrix properties involving pointedness of a category, such as the properties of a category to be unital, strongly unital or subtractive, for example. Moreover, this extended algorithm can also be used to determine whether a given matrix property is the Bourn localization of another, thus leading to new characterizations of Mal'tsev, majority and arithmetical categories. Using a computer implementation of our algorithm, we can display all such properties given by matrices of fixed dimensions, grouped according to their Bourn localizations, as well as the implications between them.

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BibTeX RIS

Michael Hoefnagel, Pierre-Alain Jacqmin. 2022-08-19. Matrix taxonomy and Bourn localization. https://arxiv.org/abs/2208.09509

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