Given a higher-rank graph , we investigate the relationship between the cohomology of and the cohomology of the associated groupoid . We define an exact functor between the Abelian category of right modules over a higher-rank graph and the category of -sheaves, where is the path groupoid of . We use this functor to construct compatible homomorphisms from both the cohomology of with coefficients in a right -module, and the continuous cocycle cohomology of with values in the corresponding -sheaf, into the sheaf cohomology of .
The current online version of this article, posted on 19 December 2017, supersedes the advance publication version posted on 10 November 2017. The affiliation and contact information for the first author have been corrected.
"Cohomology for small categories: -graphs and groupoids." Banach J. Math. Anal. 12 (3) 572 - 599, July 2018. https://doi.org/10.1215/17358787-2017-0041