nLab
parametrized spectrum

under construction

Idea

A bundle of spectra.

Specifically, for $X$ an ∞-groupoid a spectrum parameterized over $X$ is an (∞,1)-functor $X\to \mathrm{Spec}$ from $X$ to the stable (∞,1)-category of spectra.

The collection of all parameterized spectra for all $\mathrm{\infty }$-groupoids $X$ should form the tangent (∞,1)-category of ∞Grpd.

Applications

In twisted cohomology.

Related concepts

• sheaf of spectra

References

The comprehensive textbook on the matter is

• Peter May, J. Sigurdsson, Parametrized Homotopy Theory

A formulation of aspects of this in (∞,1)-category theory is in

• Matthew Ando, Andrew Blumberg, David Gepner, Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map (arXiv:1112.2203)

See also the references at (∞,1)-vector bundle.