Geodesic
Split extensions and semidirect products of unitary magmas
Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 4, pp. 509-527.

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We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.
DOI : 10.14712/1213-7243.2020.001
Classification : 08C05, 18G50, 20N02
Keywords: unitary magma; split extension; firm split extension; semidirect product 
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Gran, Marino; Janelidze, George; Sobral, Manuela. Split extensions and semidirect products of unitary magmas. Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 4, pp. 509-527. doi : 10.14712/1213-7243.2020.001. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.001/

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