The Zassenhaus lemma in star-regular categories

zbMath1428.18005arXiv1811.05876MaRDI QIDQ5243049

Florence Sterck, Olivette Ngaha Ngaha

Publication date: 14 November 2019

Full work available at URL: https://arxiv.org/abs/1811.05876

zbMATH Keywords

cocommutative Hopf algebranormal categoryideal of morphismsstar-regular categoryisomorphism theoremsideal determined categoryfactorisation systemsZassenhaus lemmagood theory of ideals

Mathematics Subject Classification ID

Epimorphisms, monomorphisms, special classes of morphisms, null morphisms (18A20) Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) (18A30) Factorization systems, substructures, quotient structures, congruences, amalgams (18A32) Categories and theories (18C99) Hopf algebras and their applications (16T05)

Cites Work

• A torsion theory in the category of cocommutative Hopf algebras
• Effective descent morphisms in star-regular categories
• Monotone-light factorisation systems and torsion theories
• A good theory of ideals in regular multi-pointed categories
• Jordan-Hölder, modularity and distributivity in non-commutative algebra
• Some remarks on Maltsev and Goursat categories
• \(3 \times 3\) lemma for star-exact sequences
• The denormalized \(3{\times}3\) lemma
• A semi-abelian extension of a theorem by Takeuchi
• Exact categories and categories of sheaves
• The Zassenhaus lemma for categories
• Jordan-Hölder theorem for finite dimensional Hopf algebras
• Notes on Extensions of Hopf Algebras
• Semi-abelian categories
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