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Indexed categories and their applications (1978)
Titre : Indexed categories and their applications Type de document : texte imprimé Editeur : Berlin : Springer-Verlag Année de publication : 1978 Collection : Lecture Note in Mathematics, ISSN 0075-8434 num. 661 Importance : IV-260 p. ISBN/ISSN/EAN : 978-3-540-08914-8 Langues : Anglais Catégories : 18A05
18C10
18D20
18D30Mots-clés : catégorie indexée Note de contenu : références Indexed categories and their applications [texte imprimé] . - Berlin : Springer-Verlag, 1978 . - IV-260 p.. - (Lecture Note in Mathematics, ISSN 0075-8434; 661) .
ISBN : 978-3-540-08914-8
Langues : Anglais
Catégories : 18A05
18C10
18D20
18D30Mots-clés : catégorie indexée Note de contenu : références Exemplaires
Code-barres Cote Support Localisation Section Disponibilité 2316 LN 661 Livre Recherche Salle Disponible On the classification of 2-gerbes and 2-stacks / Lawrence BREEN (1994)
Titre : On the classification of 2-gerbes and 2-stacks Type de document : texte imprimé Auteurs : Lawrence BREEN, Auteur Editeur : Paris : Société Mathématique de France Année de publication : 1994 Collection : Astérisque, ISSN 0303-1179 num. 225 Importance : 160 p. Langues : Anglais Catégories : 18D05
18D10
18D30
18G50
55S45Résumé : According to J. Giraud, the degree two cohomology classes of a space X with values in a non-abelian sheaf of groups describe equivalence classes of gerbes on X. We examine here the analogous concept of a 2-gerbe on a space X. It is proved that such a 2-gerbe, when suitably trivialized, is described up to equivalence by a nonabelian degree three cohomology class. An inverse construction, based on the notion of higher descent, shows that this cohomology class entirely characterizes the 2-gerbe up to equivalence. A first application of these results is a detailed description of the 2-gerbe of realizations of a lien. This embodies a vast generalization of Eilenberg and Mac Lane's well-known cohomological obstruction to the realization of an abstract kernel. Another application is the cohomological classification, it à la Postnikov, of stacks and 2-stacks with given homotopy sheaves. Finally, It is shown how this theory yields a unified approach to the problem of defining and classifying group laws (possibly constrained to satisfy appropriate commutativity conditions) on categories and 2-categories. This gives as a special case the analogous result for group laws on categories and 2-cateogries. Note de contenu : bibliogr. On the classification of 2-gerbes and 2-stacks [texte imprimé] / Lawrence BREEN, Auteur . - Paris : Société Mathématique de France, 1994 . - 160 p.. - (Astérisque, ISSN 0303-1179; 225) .
Langues : Anglais
Catégories : 18D05
18D10
18D30
18G50
55S45Résumé : According to J. Giraud, the degree two cohomology classes of a space X with values in a non-abelian sheaf of groups describe equivalence classes of gerbes on X. We examine here the analogous concept of a 2-gerbe on a space X. It is proved that such a 2-gerbe, when suitably trivialized, is described up to equivalence by a nonabelian degree three cohomology class. An inverse construction, based on the notion of higher descent, shows that this cohomology class entirely characterizes the 2-gerbe up to equivalence. A first application of these results is a detailed description of the 2-gerbe of realizations of a lien. This embodies a vast generalization of Eilenberg and Mac Lane's well-known cohomological obstruction to the realization of an abstract kernel. Another application is the cohomological classification, it à la Postnikov, of stacks and 2-stacks with given homotopy sheaves. Finally, It is shown how this theory yields a unified approach to the problem of defining and classifying group laws (possibly constrained to satisfy appropriate commutativity conditions) on categories and 2-categories. This gives as a special case the analogous result for group laws on categories and 2-cateogries. Note de contenu : bibliogr. Exemplaires
Code-barres Cote Support Localisation Section Disponibilité 15985 AST 225 Livre Recherche Salle Disponible