@INPROCEEDINGS{Jardine09cocyclecategories, author = {J. F. Jardine}, title = {Cocycle categories}, booktitle = {In Algebraic Topology}, year = {2009}, pages = {185--218}, publisher = {Springer} }

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Abstract

Suppose that G is a sheaf of groups on a space X and that Uα ⊂ X is an open covering. Then a cocycle for the covering is traditionally defined to be a family of elements gαβ ∈ G(Uα ∩ Uβ) such that gαα = e and gαβgβγ = gαγ when all elements are restricted to the group G(Uα ∩ Uβ ∩ Uγ).