Cohomology for small categories: K-graphs and groupoids

Elizabeth Gillaspy, Alexander Kumjian

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Given a higher-rank graph Λ, we investigate the relationship between the cohomology of Λ and the cohomology of the associated groupoid G Λ . We define an exact functor between the Abelian category of right modules over a higher-rank graph Λ and the category of G Λ -sheaves, where G Λ 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 G Λ with values in the corresponding G Λ -sheaf, into the sheaf cohomology of G Λ .

Original languageEnglish
Pages (from-to)572-599
Number of pages28
JournalBanach Journal of Mathematical Analysis
Issue number3
StatePublished - 2018


Kumjian's work was partially supported by Simons Foundation Collaboration grant 353626. Gillaspy's work was partially supported by the Deutsches Forschungsgemeinschaft via the project SFB 878 "Groups, Geometry, and Actions," Universität Münster.

FundersFunder number
Simons Foundation353626


    • Cohomology
    • Groupoids
    • Higher-rank graphs


    Dive into the research topics of 'Cohomology for small categories: K-graphs and groupoids'. Together they form a unique fingerprint.

    Cite this