Normalities and commutators

By Sandra Mantovani, Giuseppe Metere. 2010

49 citations recorded by the source corpus.

Abstract We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of this commutator. Our main result is to extend to any semi-abelian category the following well-known characterization of normal subgroups: a subobject K is normal in A if, and only if, [ A , K ] ⩽ K .

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1182c1e8a4be2f86c62c480317d5882af5d28165