Torsion theories in homological categories

We introduce and study the notion of torsion theory in the non-abelian context of homological categories, and we investigate the properties of the corresponding closure operator. We then consider several new examples of torsion theories in the category of topological groups and, more generally, in any category of topological semi-abelian algebras. We finally characterize the hereditary torsion theories, and we analyse a new example in the homological category of crossed modules.