natural equivalence of CG and CM categories

Theorem 0.1.

(with proof by Verdier [1]) The categoryMathworldPlanetmath CG of categorical groups and functorial homomorphismsMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath between categorical groups, and the category CM of crossed modules of groups and homomorphisms between them, are naturally equivalent.


  • 1 Jean-Louis Verdier, Des catégories dérivées des catégories abéliennes, Astérisque, vol. 239, SocietéMathematiquedeFrance,1996(inFrench).
Title natural equivalence of CG and CM categories
Canonical name NaturalEquivalenceOfCGAndCMCategories
Date of creation 2013-03-22 18:25:47
Last modified on 2013-03-22 18:25:47
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 13
Author bci1 (20947)
Entry type Theorem
Classification msc 55M05
Classification msc 18E05
Classification msc 18-00
Related topic HomotopyGroupoidsAndCrossComplexesAsNonCommutativeStructuresInHigherDimensionalAlgebraHDA
Related topic EquivalenceOfCategories2
Related topic FunctorCategory2
Related topic GroupCohomology
Related topic IndexOfCategories