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Categorical properties of cocommutative Hopf algebras

Geenis, Logan
(2025)

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Details

Supervisors
Gran, Marino
Faculty
Faculté des sciences
Degree label
Master [120] en sciences mathématiques, à finalité approfondie
Abstract
enIn the first chapter, the notion of a semi-abelian category is introduced, first in its most recent form, and then through its "older" axioms. Furthermore, the equivalence between these two forms is proven. In the second chapter, the category of cocommutative Hopf algebras is introduced, and, to link it with the first chapter, it is also proven that this category satisfies the definition of a semi-abelian category. The third and final chapter deals with the characteristic subobject. This chapter aims to show that the commutator of two characteristic subobjects in the category of cocommutative Hopf algebras is also characteristic. To do so, notions such as algebraically coherent categories and the commutators of Smith, Higgins, and Huq are introduced.