Remark 3.2.5. After constructing the tensor product of spectra, we will associate to \(E\) a reduced homology theory by the formula \[ \widetilde E_k(X):=\pi _k(\Sigma ^{\infty }X\otimes E); \] we refer to Subsection 4.4.5 for details. The idea of using spectra to define homology and cohomology theories, and with it the notion of a generalized homology theory, goes back to Whitehead (1962).
Generated from the authoritative LaTeX source.