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Topological protomodular algebras
Borceux, F.; Clementino, Maria ManuelTopological groups have very striking properties, which have already been generalized to weaker "group like" structures, like various kinds of loops. This paper intends to show evidence that this generalization holds for a much wider class of theories, known as the protomodular theories, and which admit both an elegant categorical characterization and an easy description in universal algebra terms. Thus we prop...
Prolocalisations of homological categories
Borceux, F.; Clementino, M. M.; Gran, M.; Sousa, L.A prolocalisation of an homological (resp. semi-abelian) category is a regular full re ective subcategory, whose re ection preserves short exact sequences. We study the closure operator and the torsion theory associated with such a situation. We pay special attention to the bered, the epire ective and the monore ective cases. We give examples in algebra, topos theory, functional analysis. ; Université Catho...
Topological semi-abelian algebras
Borceux, F.; Clementino, Maria ManuelGiven an algebraic theory whose category of models is semi-abelian, we study the category of topological models of and generalize to it most classical results on topological groups. In particular, is homological, which includes Barr regularity and forces the Mal'cev property. Every open subalgebra is closed and every quotient map is open. We devote special attention to the Hausdorff, compact, locally compact, c...
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