Vol. 91, No. 2, 1980

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ISSN: 0030-8730
Cohomology of diagrams and equivariant singular theory

Robert John Piacenza

Vol. 91 (1980), No. 2, 435–443
Abstract

The purpose of this paper is to define a cohomology theory for diagrams of simplicial sets that specializes to Illman’s equivariant singular cohomology for discrete G. We show that such a theory is representable by a suitable Eilenberg-Maclane object. The paper concludes with a comparison of equivariant singular cohomology and equivariant sheaf cohomology.

We adopt the category theory of Maclane as formulated in “Categories for the working mathematician” and use the framework of Quillen’s “Homotopical Algebra.”

Mathematical Subject Classification 2000
Primary: 55N35
Secondary: 55S99
Milestones
Received: 2 October 1979
Revised: 9 July 1980
Published: 1 December 1980
Authors
Robert John Piacenza