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arXiv · 1403.5873

On $2$-star-permutability in regular multi-pointed categories

Marino Gran·Diana Rodelo
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Abstract

$2$-star-permutable categories were introduced in a joint work with Z. Janelidze and A. Ursini as a common generalisation of regular Mal'tsev categories and of normal subtractive categories. In the present article we first characterise these categories in terms of what we call star-regular pushouts. We then show that the $3 \times 3$ Lemma characterising normal subtractive categories and the Cuboid Lemma characterising regular Mal'tsev categories are special instances of a more general homological lemma for star-exact sequences. We prove that $2$-star-permutability is equivalent to the validity of this lemma for a star-regular category.

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Marino Gran, Diana Rodelo. 2014-03-24. On $2$-star-permutability in regular multi-pointed categories. https://doi.org/10.1142/s0219498814500686

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