External Spanier-Whitehead duality and homology representation theorems for diagram spaces

Abstract

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 by taking the homotopy groups of a balanced smash product with a fixed ${\mathcal{C}}^{\mathrm{op}}$-spectrum. We use this to construct Chern characters for certain rational $\mathcal{C}$-homology theories.

arXiv comment45 pages

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Cited by in corpus (1)

• Sufficient and necessary conditions for hereditary of infinite category algebras