natural equivalence of $C_G$ and $C_M$ categories

Theorem 0.1.

(with proof by Verdier [1]) The category ${\mathrm{C}}_G$ of categorical groups and functorial homomorphisms between categorical groups, and the category ${\mathrm{C}}_M$ of crossed modules of groups and homomorphisms between them, are naturally equivalent.

Title	natural equivalence of $C_G$ and $C_M$ 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