# The Zassenhaus lemma in star-regular categories

## Olivette Ngaha Ngaha and Florence Sterck

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 previously considered by O.~Wyler, by working in the framework of \emph{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.

Keywords: Factorisation systems, ideal of morphisms, normal category, star-regular category, ideal determined category, good theory of ideals, isomorphism theorems, Zassenhaus lemma, cocommutative Hopf algebra

2010 MSC: 18A20, 18A30, 18A32, 18C99, 16T05

Theory and Applications of Categories, Vol. 34, 2019, No. 38, pp 1196-1219.

Published 2019-11-12.

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