No subtopics of Category Theory
- Fundamental group of Schurian categories and the Hurewicz isomorphism
- On the duality between trees and disks
- A universal characterization of higher algebraic K-theory
- Graded nilpotent Lie algebras of infinite type
Normalities and Commutators
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, $[A,K]\leq K$.
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