If H is a G-crossed module, the set of derivations of G in 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.
External derivations of internal groupoids / S. Kasangian, S. Mantovani, G. Metere, E.M. Vitale. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 212:1(2008 Jan), pp. 175-192.
External derivations of internal groupoids
S. KasangianPrimo
;S. MantovaniSecondo
;G. MeterePenultimo
;
2008
Abstract
If H is a G-crossed module, the set of derivations of G in 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.File | Dimensione | Formato | |
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