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.
Kasangian, S., Mantovani, S., Metere, G., Vitale, E. (2008). External derivations of internal groupoids. JOURNAL OF PURE AND APPLIED ALGEBRA, 212(1), 175-192 [10.1016/j.jpaa.2007.05.013].
External derivations of internal groupoids
METERE, Giuseppe;
2008-01-01
Abstract
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.
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