Stefan Schwede

Algebras and Modules in Monoidal Model Categories

In recent years the theory of structured ring spectra (formerly known as A

MODEL CATEGORIES OF DIAGRAM SPECTRA

_{\infty}

Stable model categories are categories of modules

- and E

Equivalences of monoidal model categories

_{\infty}

Spectra in model categories and applications to the algebraic cotangent complex

-ring spectra) has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products. Now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra. In this paper we provide a general method for constructing model category structures for categories of ring, algebra, and module spectra. This provides the necessary input for obtaining model categories of symmetric ring spectra, functors with smash product,

Stable homotopy of algebraic theories

\Gamma

S-modules and symmetric spectra

-rings, and diagram ring spectra. Algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra. 1991 Mathematics Subject Classification: primary 55U35; secondary 18D10.

Realizability of modules over Tate cohomology

Working in the category

Triangulated categories without models

\mathcal{T}

Structured Ring Spectra: Morita theory in abelian, derived and stable model categories

of based spaces, we give the basic theory of diagram spaces and diagram spectra. These are functors