Peiffer product and Peiffer commutator for internal pre-crossed modules

Description:  In this work we introduce the notions of Peiffer product and Peiffer commutator of internal pre-crossed modules over a fixed object B, extending the corresponding classical notions to any semi-abelian category. We prove that, under mild additional assumptions on the category, crossed modules are characterized as those pre-crossed modules whose Peiffer commutator is trivial. Furthermore we provide suitable conditions on the ground category (fulfilled by a large class of algebraic varietes, including among others associative algebras, Lie and Leibniz algebras) under which the Peiffer product realizes the coproduct in the category of crossed modules over B. Date:  2015-03-24 Start Time:   14:30 Speaker:  Alan S. Cigoli (Università degli Studi di Milano, Italy) Institution:  Università degli Studi di Milano Place:  Sala 5.5 Research Groups: -Algebra, Logic and Topology See more:   <Main>