Abstract
If G is a categorical group, a G -module is defined to be a braided categorical group ( A , c ) together with an action of G on ( A , c ) . We associate to any G -module ( A , c ) a Kan simplicial set Ner ( G ( A , c ) ) and a Kan fibration Ner ( G ( A , c ) ) → ϕ Ner ( G ) . In addition, we define the set of equivalence classes of singular extensions of G by ( A , c ) , and also a 1-cohomology set of G with coefficients in ( A , c ) . We construct bijections between these sets, and also with the set of fibre homotopy classes of cross-sections of the fibration φ.
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Schedule a callMore From: Comptes Rendus de l'Academie des Sciences Series I Mathematics
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