Resolutions, relation modules and Schur multipliers for categories

Peter Webb

doi:10.1016/j.jalgebra.2009.05.022

Resolutions, relation modules and Schur multipliers for categories

Peter Webb

Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

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 language	English (US)
Pages (from-to)	245-276
Number of pages	32
Journal	Journal of Algebra
Volume	326
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2009.05.022
State	Published - Jan 15 2011

Keywords

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

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KW - Five-term exact sequence

KW - Gruenberg resolution

KW - Schur multiplier

KW - Stem extension

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Resolutions, relation modules and Schur multipliers for categories

Abstract

Keywords

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