Cohomology for small categories: K-graphs and groupoids

Elizabeth Gillaspy, Alexander Kumjian

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume12
Issue number3
DOIs
StatePublished - 2018

Keywords

  • Cohomology
  • Groupoids
  • Higher-rank graphs

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