Search results for "Accessible category"

showing 2 items of 2 documents

Obstruction theory in action accessible categories

2013

Abstract We show that, in semi-abelian action accessible categories (such as the categories of groups, Lie algebras, rings, associative algebras and Poisson algebras), the obstruction to the existence of extensions is classified by the second cohomology group in the sense of Bourn. Moreover, we describe explicitly the obstruction to the existence of extensions in the case of Leibniz algebras, comparing Bourn cohomology with Loday–Pirashvili cohomology of Leibniz algebras.

Algebra and Number TheoryGroup (mathematics)Accessible categoryAction accessible categorieObstruction theoryMathematics::Algebraic TopologyAction accessible categoriesCohomologyAction (physics)Action accessible categories; Leibniz algebras; Obstruction theoryLeibniz algebraAlgebraSettore MAT/02 - AlgebraMathematics::K-Theory and HomologyMathematics::Category TheoryLie algebraObstruction theoryLeibniz algebrasAssociative propertyObstruction theorymatMathematics
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A Push Forward Construction and the Comprehensive Factorization for Internal Crossed Modules

2014

In a semi-abelian category, we give a categorical construction of the push forward of an internal pre-crossed module, generalizing the pushout of a short exact sequence in abelian categories. The main properties of the push forward are discussed. A simplified version is given for action accessible categories, providing examples in the categories of rings and Lie algebras. We show that push forwards can be used to obtain the crossed module version of the comprehensive factorization for internal groupoids.

Exact sequenceAlgebra and Number TheoryGeneral Computer ScienceSemi-abelian categoryAccessible categoryPushoutCrossed moduleCrossed modulecrossed module push forward comprehensive factorizationTheoretical Computer ScienceAlgebraSettore MAT/02 - AlgebraComprehensive factorizationFactorizationMathematics::Category TheoryLie algebraPush forwardAbelian groupComprehensive factorization; Crossed module; Push forward; Semi-abelian categoryCategorical variableMathematicsApplied Categorical Structures
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