The homotopy category of parametrized spectra (Q761658)

The authors construct a homotopy category of spectra parametrized over a space B convenient for applications. The objects are coordinate free spectra (over B) indexed by inner product spaces. A symmetric monoidal category structure is obtained with the smash product as multiplication and the zero sphere as unit object. They work entirely in the category of weakly Hausdorff, compactly generated spaces. The construction has already been given in the first author's doctoral dissertation (Heidelberg 1979), extending to the general case a description for B a point given by the second author (mimeographed notes 1975). As a corollary they obtain also a symmetric monoidal category structure of parametrized spectra over B indexed by the natural numbers.