A. R. Garzon, A. del Rio

The Whitehead Categorical Group of Derivations

Given a categorical crossed module H --> G, where G is a group, we show that the category of derivations, Der(G, H), from G into H has a natural monoidal structure. We introduce the Whitehead categorical group of derivations as the Picard category of Der(G, H) and then we characterize the invertible derivations, with respect to the tensor product, in this monoidal category.