Homotopy classification of gerbes
Jardine, J. F. (University of Western Ontario (Canadà). Mathematics Department)

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 ; publishedVersion
Matèria: Gerbes ; Cocycles ; 2-groupoids ; Simplicial presheaves
Publicat a: Publicacions Matemàtiques, V. 54 n. 1 (2010) p. 83-111, ISSN 0214-1493

Adreça original: http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565-PUBLMAT_54110_05
DOI: 10.5565/PUBLMAT_54110_05
DOI: 10.5565/154818

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