A categorical approach to internal actions and semidirect products

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.