Stable homotopy theory
Stable Homotopy theory
A function spectrum or mapping spectrum is the analog of a mapping space in the context of stable homotopy theory. It makes the stable homotopy category into a closed category, and together with the smash product of spectra into a smmyetric closed monoidal category
Given two spectra and , their function spectrum is the internal hom in a suitable category of spectra.
In the context of generalized (Eilenberg-Steenrod) cohomology the generalized -cohomology of a topological space is given by the homotopy groups of the mapping spectrum .
- Harold Hastings, On function spectra, Proceedings of the AMS, volume 44, Number 1, May 1974 (pdf)
For symmetric spectra:
Revised on July 7, 2016 09:09:13
by Urs Schreiber