0000000000395508

AUTHOR

Andrea Montoli

0000-0002-7016-3716

showing 2 related works from this author

Semidirect products of internal groupoids

2010

We give a characterization of those finitely complete categories with initial object and pushouts of split monomorphisms that admit categorical semidirect products. As an application we examine the case of groupoids with fixed set of objects. Further, we extend this to the internal case. (C) 2010 Elsevier B.V. All rights reserved.

Set (abstract data type)AlgebraSettore MAT/02 - AlgebraHigher-dimensional algebraAlgebra and Number Theorysemi-direct product groupoid internal structuresMathematics::Category TheoryCharacterization (mathematics)Categorical variableInitial and terminal objectsMathematicsJournal of Pure and Applied Algebra
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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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