The Zassenhaus lemma in star-regular categories
Olivette Ngaha Ngaha, Florence Sterck
TL;DR
This paper extends the Zassenhaus Lemma and Noether isomorphism theorems to star-regular categories, unifying pointed and non-pointed categorical contexts, with detailed examples of applicable categories.
Contribution
It introduces a unified categorical framework for the Zassenhaus Lemma and related theorems using star-regular categories, bridging pointed and non-pointed cases.
Findings
Generalization of Zassenhaus Lemma to star-regular categories
Unification of pointed and non-pointed categorical results
Concrete examples of categories satisfying the conditions
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra