Topological semi-abelian algebras
Abstract: 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 various results on topological groups. In particular
Top^T is regular, Mal'cev and protomodular; every open subobject 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.
