Brown Representability and Spaces over a Category

@inproceedings{Brcenas2014BrownRA,
  title={Brown Representability and Spaces over a Category},
  author={No{\'e} B{\'a}rcenas},
  year={2014}
}
We prove a Brown Representability Theorem in the context of spaces over a category. We discuss two applications to the representability of equivariant cohomology theories, with emphasis on Bredon cohomology with local coefficients. 
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Background Citations
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2 Citations

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References

SHOWING 1-10 OF 15 REFERENCES
Equivariant cohomology with local coefficients
We show that for a discrete group G, the equivariant cohomology of a G-space X with G-local coefficients M is isomorphic to the Bredon-Illman cohomology of X with equivariant local coefficients M.
Representing Bredon cohomology with local coefficients
Equivariant Cohomological Chern Characters
  • W. Lück
  • Mathematics
    Int. J. Algebra Comput.
  • 2005
TLDR
It is shown that the coefficients of the equivariant cohomology theory possess a Mackey structure, which is present in many interesting examples, and this structure can be assigned to CW-complexes.
Segal's Spectral Sequence in Twisted Equivariant K-theory for Proper and Discrete Actions
Abstract We use a spectral sequence developed by Graeme Segal in order to understand the twisted G-equivariant K-theory for proper and discrete actions. We show that the second page of this spectral…
Steenrod's operations in simplicial Bredon-Illman cohomology with local coefficients
In this paper we use Peter May’s algebraic approach to Steenrod operations to construct Steenrod’s reduced power operations in simplicial Bredon-Illman cohomology with local coefficients of a one…
The equivariant Serre spectral sequence
For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new…
Steenrod ∪i-products on Bredon–Illman cohomology
The Grothendieck duality theorem via Bousfield’s techniques and Brown representability
Grothendieck proved that if f: X ) Y is a proper morphism of nice schemes, then Rf* has a right adjoint, which is given as tensor product with the relative canonical bundle. The original proof was by…
Categories for the Working Mathematician
I. Categories, Functors and Natural Transformations.- 1. Axioms for Categories.- 2. Categories.- 3. Functors.- 4. Natural Transformations.- 5. Monics, Epis, and Zeros.- 6. Foundations.- 7. Large…
Equivariant Homotopy and Cohomology Theory
...
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