Georgian Mathematical Journal 09 (2002), No. 4, 709--721
Copyright Heldermann Verlag 2002
The Whitehead Categorical Group of Derivations
A. R. Garzon
Dep. de Algebra, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
A. del Rio
Dep. de Algebra, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
[Abstract-pdf]
Given a categorical crossed module ${\mathbb H}\rightarrow G$, where $G$ is a group, we show that the category of derivations, $Der(G,{\mathbb H})$, from $G$ into ${\mathbb H}$ has a natural monoidal structure. We introduce the Whitehead categorical group of derivations as the Picard category of $Der(G,{\mathbb H})$ and then we characterize the invertible derivations, with respect to the tensor product, in this monoidal category.
Keywords: Derivation, monoidal category, categorical group, crossed module.
MSC: 18D10, 20J05
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