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A categorical approach to internal actions and semidirect products

Deval, Bo Shan
(2022)

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Deval_19041700_2022.pdf
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Details

Supervisors
Van der Linden, Tim
Faculty
Faculté des sciences
Degree label
Master [120] en sciences mathématiques, à finalité approfondie
Abstract
Actions are an important concept in mathematics; in this thesis, we present a theory of internal actions. This work follows the algebraic examples of actions of groups and commutative rings before going to the generalisation of the concept of internal actions in semi-abelian categories. The main result we present is the equivalence between internal actions and split short exact sequences via a semidirect product construction, which allows to generalise some well-known actions such as trivial actions and conjugation actions in a semi-abelian context.