Spanier-Whitehead duality
= Spanier-Whitehead duality
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For a <finite spectrum> $A$, evaluation and coevaluation identify $[B,D\wedge A]_{\mathrm{st}}$ with $[B\wedge A^\vee,D]_{\mathrm{st}}$. Cellular induction constructs the dual from the duals of stable cells and verifies these identities across <cofiber sequences of spectra>. In particular $\pi_k(D\wedge A)=[\Sigma^kA^\vee,D]_{\mathrm{st}}$.