The Zassenhaus lemma in star-regular categories

Abstract

The Noether isomorphism theorems and the Zassenhaus Lemma from group theory have a non-pointed version in a suitable categorical context first considered by W. Tholen in his PhD thesis. This article leads to a unification of these results with the ones in the pointed categorical context considered by O. Wyler, by working in the framework of star-regular categories introduced by M. Gran, Z. Janelidze and A. Ursini. Some concrete examples of categories where these results hold are examined in detail.

arXiv comment24 pages

References in corpus (3)

• A semi-abelian extension of a theorem by Takeuchi
• A torsion theory in the category of cocommutative Hopf algebras
• Monotone-light factorisation systems and torsion theories