We investigate what is remaining of the 3 × 3 lemma and of the denormalized 3 × 3 lemma, valid in a pointed protomodular and in a Mal'tsev category, respectively, in the context of partial pointed protomodular and partial Mal'tsev categories, relatively to a class Σ of points (i.e. of split epimorphisms with a fixed section). The results apply, among other structures, to monoids, semirings, and quandles.
The 3 × 3 lemma in the Σ-Mal'tsev and Σ-protomodular settings : Applications to monoids and quandles / D. Bourn, A. Montoli. - In: HOMOLOGY, HOMOTOPY AND APPLICATIONS. - ISSN 1532-0073. - 21:2(2019 Apr 03), pp. 305-332. [10.4310/HHA.2019.V21.N2.A17]
The 3 × 3 lemma in the Σ-Mal'tsev and Σ-protomodular settings : Applications to monoids and quandles
A. Montoli
2019
Abstract
We investigate what is remaining of the 3 × 3 lemma and of the denormalized 3 × 3 lemma, valid in a pointed protomodular and in a Mal'tsev category, respectively, in the context of partial pointed protomodular and partial Mal'tsev categories, relatively to a class Σ of points (i.e. of split epimorphisms with a fixed section). The results apply, among other structures, to monoids, semirings, and quandles.
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