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natural equivalence of $C_G$ and $C_M$ categories (Theorem)

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

Bibliography

1
Jean-Louis Verdier, Des catégories dérivées des catégories abéliennes, Astérisque, vol. 239, Société Mathématique de France, 1996 (in French).



"natural equivalence of $C_G$ and $C_M$ categories" is owned by bci1.
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See Also: homotopy groupoids and crossed complexes: non-commutative structures in higher dimensional algebra (HDA), natural equivalence of categories, functor category, group cohomology, index of categories

Keywords:  category equivalence, category of categorical groups and functorial homomorphisms, category CM of crossed modules of groups and homomorphisms
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Cross-references: naturally equivalent, modules, homomorphisms, groups, categorical, category, proof, theorem
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This is version 8 of natural equivalence of $C_G$ and $C_M$ categories, born on 2008-09-24, modified 2009-01-07.
Object id is 11085, canonical name is NaturalEquivalenceOfC_GAndC_MCategories.
Accessed 396 times total.

Classification:
AMS MSC: 18-00 (Category theory; homological algebra :: General reference works )
 18E05 (Category theory; homological algebra :: Abelian categories :: Preadditive, additive categories)
 55M05 (Algebraic topology :: Classical topics :: Duality)
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