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Cerca | Lliura | Ajuda | Servei de Biblioteques | Sobre el DDD | Català English Español |
Pàgina inicial > Articles > Articles publicats > Homotopy classification of gerbes |
Data: | 2010 |
Resum: | Gerbes are locally connected presheaves of groupoids on a small Grothendieck site C. They are classified up to local weak equivalence by path components of a cocycle category taking values in the big 2-groupoid Iso(Gr(C)) consisting of all sheaves of groups on C, their isomorphisms and homotopies. If F is a full sub- presheaf of Iso(Gr(C)) then the set [*,BF] of morphisms in the homotopy category of simplicial presheaves classifies gerbes locally weakly equivalent to objects of F. Id St(пF)is the stack completion of the fundamental groupoid(пF)of F if L is a global section of St(пF) and if FL is the homotopy fibre over L of the canonical map BF --> B St(пF), then [*FL] is in bijective correspondence with Giraud's non-abelian cohomology object H2 (C, L) of equivalence classes of gerbes with band L. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Matèria: | Gerbes ; Cocycles ; 2-groupoids ; Simplicial presheaves |
Publicat a: | Publicacions matemàtiques, V. 54 n. 1 (2010) p. 83-111, ISSN 2014-4350 |
29 p, 264.9 KB |