stable (infinity,1)-category of spectra
Stable Homotopy theory
The collection of spectra form an (∞,1)-category which is in fact a stable (∞,1)-category. Indeed, it is the universal property stabilization of the -category ∞Grpd, equivalently of the simplicial localization of the category Top at the weak homotopy equivalences.
plays a role in stable homotopy theory analogous to the role played by the 1-category Ab of abelian groups in homological algebra, or rather of the category of chain complexes of abelian groups.
In the context of (∞,1)-categories a spectrum is a spectrum object in the (∞,1)-category of pointed topological spaces.
Recall that spectrum objects in the (infinity,1)-category form a stable (∞,1)-category .
The stable (∞,1)-category of spectrum objects in is the stable -category of spectra
Prime spectrum and Morava K-theory
The prime spectrum of a monoidal stable (∞,1)-category for p-local and finite spectra is labeled by the Morava K-theories. This is the content of the thick subcategory theorem.
the stable -category of spectra is described in section 9 of
Its monoidal structure is described in section 4.2
That this is a symmetric monoidal structure is described in section 6 of
Revised on March 24, 2014 07:14:35
by Urs Schreiber