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RESEARCH PRODUCT
Normalities and Commutators
Giuseppe MetereSandra Mantovanisubject
Normal subgroupPure mathematicsmedia_common.quotation_subjectCharacterization (mathematics)law.inventionSemi-abelianNormal subobjectlawCommutatorMathematics::Category TheorySubobjectFOS: MathematicsIdeal (order theory)Category Theory (math.CT)Algebraic numberCategorical variableNormalityMathematicsmedia_commonDiscrete mathematicsAlgebra and Number TheoryCommutator (electric)Mathematics - Category TheoryIdealSettore MAT/02 - Algebra08A30 18A20 08A50description
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. (C) 2010 Elsevier Inc. All rights reserved.}
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-02-08 |