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New Wide Classes of Weakly Mal’tsev Categories

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Abstract

The following classes of categories are shown to be weakly Mal’tsev in the sense of the author: (i) a suitable class of algebras with cancellation; (ii) the dual of any quasi-adhesive category; (iii) the dual of any extensive category with pullback-stable epimorphisms; (iv) the dual of any solid quasi-topos. The examples in (i) include all the Mal’tsev varieties of algebras such as groups, rings, Lie algebras, etc., but also distributive lattices and commutative monoids with cancellation. The examples in (ii)-(iv) capture many of the familiar aspects of topological spaces.

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  1. Escola Superior de Tecnologia e Gestão, Centro para o Desenvolvimento Rápido e Sustentado do Produto, Instituto Politécnico de Leiria, 2411-901, Leiria, Portugal

    Nelson Martins-Ferreira

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Martins-Ferreira, N. New Wide Classes of Weakly Mal’tsev Categories. Appl Categor Struct 23, 741–751 (2015). https://doi.org/10.1007/s10485-014-9377-4

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