Abstract
Given a higher-rank graph Λ, we investigate the relationship between the cohomology of Λ and the cohomology of the associated groupoid GΛ. We define an exact functor between the Abelian category of right modules over a higher-rank graph Λ and the category of GΛ-sheaves, where GΛ is the path groupoid of Λ. We use this functor to construct compatible homomorphisms from both the cohomology of Λ with coefficients in a right Λ-module, and the continuous cocycle cohomology of GΛ with values in the corresponding GΛ-sheaf, into the sheaf cohomology of GΛ.
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