Centrality and normality in protomodular categories.
Homology of -fold groupoids.
Galois theory and double central extensions.
Semi-abelian monadic categories.
-permutable locally finitely presentable categories.
Localizations of Maltsev varieties.
Protolocalisations of exact Mal'cev categories.
On the characterization of Jonsson-Tarski and of subtractive varieties
A universal construction in Goursat categories
Relative commutator associated with varieties of -nilpotent and of -solvable groups
In this note we determine explicit formulas for the relative commutator of groups with respect to the subvarieties of -nilpotent groups and of -solvable groups. In particular these formulas give a characterization of the extensions of groups that are central relatively to these subvarieties.
Split extensions and semidirect products of unitary magmas
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.
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