6533b82ffe1ef96bd129474d

RESEARCH PRODUCT

Peiffer product and peiffer commutator for internal pre-crossed modules

Sandra MantovaniAlan S. CigoliGiuseppe Metere

subject

Large classPure mathematicssemi-abelian categoryCrossed module01 natural scienceslaw.inventionMathematics (miscellaneous)law0103 physical sciencesFOS: MathematicsSemi-abelian categoryCategory Theory (math.CT)0101 mathematicsAlgebraic numberAssociative propertyMathematicsPeiffer commutator010102 general mathematicsCoproductCommutator (electric)Mathematics - Category Theorycrossed moduleProduct (mathematics)010307 mathematical physicscrossed module; Peiffer commutator; semi-abelian category

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 C. We prove that, under mild additional assumptions on C, crossed modules are characterized as those pre-crossed modules X whose Peiffer commutator 〈X, X〉 is trivial. Furthermore we provide suitable conditions on C (fulfilled by a large class of algebraic varieties, including among others groups, associative algebras, Lie and Leibniz algebras) under which the Peiffer product realizes the coproduct in the category of crossed modules over B.

yearjournalcountryeditionlanguage
2017-01-01
10.4310/hha.2017.v19.n1.a10http://hdl.handle.net/10447/226055