On 2-star-permutability in regular multi-pointed categories
(2014) Journal of Algebra and its Applications — Vol. 13, n° 8 (2014)
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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 rst characterise these categories in terms of what we call star-regular pushouts. We then show that the 3 × 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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Gran, M., & Rodelo, D. (2014). On 2-star-permutability in regular multi-pointed categories. Journal of Algebra and its Applications, 13(8). https://doi.org/10.1142/S0219498814500686 (Original work published 2014)