Resolutions, relation modules and Schur multipliers for categories

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We show that the construction in group cohomology of the Gruenberg resolution associated to a free presentation and the resulting relation module can be copied in the context of representations of categories. We establish five-term exact sequences in the cohomology of categories and go on to show that the Schur multiplier of the category has properties which generalize those of the Schur multiplier of a group.

Original languageEnglish (US)
Pages (from-to)245-276
Number of pages32
JournalJournal of Algebra
Issue number1
StatePublished - Jan 15 2011


  • Augmentation ideal
  • Category cohomology
  • Category representation
  • Five-term exact sequence
  • Gruenberg resolution
  • Schur multiplier
  • Stem extension


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