0000000000648720

AUTHOR

Stefano Kasangian

showing 2 related works from this author

External derivations of internal groupoids

2008

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.

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 productJournal of Pure and Applied Algebra
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Split extensions, semidirect product and holomorph of categorical groups

2006

Working in the context of categorical groups, we show that the semidirect product provides a biequivalence between actions and points. From this biequivalence, we deduce a two-dimensional classification of split extensions of categorical groups, as well as the universal property of the holomorph of a categorical group. We also discuss the link between the holomorph and inner autoequivalences.

Semidirect product18D05categorical groupsGroup (mathematics)split extensionssplit extension18D10Context (language use)18G5018D35AlgebraMathematics (miscellaneous)HolomorphMathematics::Category TheoryholomorphUniversal propertysemidirect productcategorical groupLink (knot theory)Categorical variableMathematics
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