Abstract
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We construct a Spanier–Whitehead type duality functor relating finite
–spectra to finite
–spectra and prove
that every
–homology
theory is given by taking the homotopy groups of a balanced smash product with a fixed
–spectrum.
We use this to construct Chern characters for certain rational
–homology
theories.
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Keywords
spaces over a category, $\mathcal{C}$–homology theories,
representation theorems, external Spanier–Whitehead
duality, Chern character
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Mathematical Subject Classification
Primary: 55N91
Secondary: 18A25, 55M05, 55P42, 55P62
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Publication
Received: 16 December 2020
Revised: 3 September 2021
Accepted: 17 October 2021
Published: 27 March 2023
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