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July 2018 Cohomology for small categories: k-graphs and groupoids
Elizabeth Gillaspy, Alexander Kumjian
Banach J. Math. Anal. 12(3): 572-599 (July 2018). DOI: 10.1215/17358787-2017-0041

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.

Version Information

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.

Citation

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Elizabeth Gillaspy. Alexander Kumjian. "Cohomology for small categories: k-graphs and groupoids." Banach J. Math. Anal. 12 (3) 572 - 599, July 2018. https://doi.org/10.1215/17358787-2017-0041

Information

Received: 9 February 2017; Accepted: 2 May 2017; Published: July 2018
First available in Project Euclid: 10 November 2017

zbMATH: 06946071
MathSciNet: MR3824741
Digital Object Identifier: 10.1215/17358787-2017-0041

Subjects:
Primary: 18B40
Secondary: 22E41, 46L05, 55N30

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.12 • No. 3 • July 2018
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