New Wide Classes of Weakly Mal’tsev Categories

Martins-Ferreira, Nelson

http://hdl.handle.net/10400.8/13310

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Authors

Martins-Ferreira, Nelson

Abstract(s)

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. © 2014, Springer Science+Business Media Dordrecht.

Keywords

Extensive category Local coproduct Pullback-stable epimorphism Quasi-adhesive category Solid quasi-topos Stable coproduct Topological space Van Kampen square Weakly Mal’tsev category

URI

http://hdl.handle.net/10400.8/13310

Citation

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