6533b829fe1ef96bd128a2d8

RESEARCH PRODUCT

External derivations of internal groupoids

Enrico VitaleSandra MantovaniGiuseppe MetereStefano Kasangian

subject

Higher-dimensional algebraAlgebra and Number TheoryComplete categoryCategory of groupsContext (language use)derivations crossed modules internal groupoids holomorphismsAlgebraSettore MAT/02 - AlgebraMathematics::K-Theory and HomologyMathematics::Category TheoryMonoid (category theory)EmbeddingAffine transformationMathematics::Symplectic GeometryMathematicsWhitehead product

description

If His a G-crossed module, the set of derivations of Gin H is a monoid under the Whitehead product of derivations. We interpret the Whitehead product using the correspondence between crossed modules and internal groupoids in the category of groups. Working in the general context of internal groupoids in a finitely complete category, we relate derivations to holomorphisms, translations, affine transformations, and to the embedding category of a groupoid. (C) 2007 Elsevier B.V. All rights reserved.

yearjournalcountryeditionlanguage
2008-01-01Journal of Pure and Applied Algebra
10.1016/j.jpaa.2007.05.013http://dx.doi.org/10.1016/j.jpaa.2007.05.013