# 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.
2 Citations
The Completion Theorem in twisted equivariant $K$-Theory for proper and discrete actions
• Mathematics
• 2014
We compare different algebraic structures in twisted equivariant K-Theory for proper actions of discrete groups. After the construction of a module structure over untwisted equivariant K-Theory, we
External Spanier-Whitehead duality and homology representation theorems for diagram spaces
We construct a Spanier-Whitehead type duality functor relating finite $\mathcal{C}$-spectra to finite $\mathcal{C}^{\mathrm{op}}$-spectra and prove that every $\mathcal{C}$-homology theory is given

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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