Obstruction theory in action accessible categories
- Authors: Cigoli, A.; Metere, G.; Montoli, A.
- Publication year: 2013
- Type: Articolo in rivista (Articolo in rivista)
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.