 Represented cohomology theory (source code)

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= Represented cohomology theory
{title2=$\widetilde E^*(X)$}

= Represented cohomology theories
{synonym}

A <topological spectrum> $E$ represents the reduced <generalized cohomology theory> $\widetilde E^q(X)=[\Sigma^\infty X,\Sigma^qE]_{\mathrm{st}}$. For an <Omega-spectrum> this equals $[X,E_q]_*$, taking $E_q=\Omega^{-q}E_0$ for negative $q$. It is contravariant in $X$.

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