Applications of Commutators and Actions in Semi-Abelian Categories
(2026)
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- Abstract
- 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.
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Deval, B. S. (2026). Applications of Commutators and Actions in Semi-Abelian Categories. https://hdl.handle.net/2078.5/281479