Webb, Peter2008-09-152008-09-152008-09-15https://hdl.handle.net/11299/43122We 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.enalgebracategoryrepresentationresolutionPreprint