Francis Borceux; Maria Manuel Clementino;
Topological semi-abelian algebras
Given an algebraic theory T whose category of models is semi-abelian, we study the category Top^T of topological models of T and generalize to it most classical results on topological groups. In particular Top^T 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, connected, totally disconnected and profinite T-algebras.
Advances in Mathematics