Applications of Commutators and Actions in Semi-Abelian Categories by Bo Shan Deval -
Mardi 22 septembre 2026 à 17h00 - Auditoire CYCL01 - Bâtiment de Hemptinne - Chemin du Cyclotron, 2 - 1348 Louvain-la-Neuve -
In this thesis, we develop three lines of investigation around actions and commutators in semi-abelian categories. In the first chapter, we lay the foundations of a theory of commutators twisted by an internal action and apply it to a characterisation of internal crossed modules. The second chapter introduces an intrinsic notion of tensor product—the bilinear product, a cosmash product computed in the two-nilpotent core—and uses it to prove a categorical version of Ganea’s theorem in homology. Finally, in the last chapter, we describe a categorical procedure towards a universal Kaluzhnin–Krasner embedding theorem and carried it out for groups and for precrossed modules.
Jury members :
Prof. Tim Van der Linden (UCLouvain) (Supervisor)
Prof. Pierre-Emmanuel Caprace (UCLouvain) (Chairperson)
Prof. Marino Gran (UCLouvain) (Secretary)
Prof. Tomas Everaert (VUB)
Prof. Diana Rodelo (Universidade do Algarve)
