Algebras and Modules in Monoidal Model Categories (1998)
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| Venue: | Proc. London Math. Soc |
| Citations: | 124 - 26 self |
BibTeX
@ARTICLE{Schwede98algebrasand,
author = {Stefan Schwede and Brooke E. Shipley},
title = {Algebras and Modules in Monoidal Model Categories},
journal = {Proc. London Math. Soc},
year = {1998},
volume = {80},
pages = {491--511}
}
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Abstract
In recent years the theory of structured ring spectra (formerly known as A # - and E # -ring spectra) has been signicantly simplified by the discovery of categories of spectra with strictly associative and commutative smash products. Now a ring spectrum can simply be dened as a monoid with respect to the smash product in one of these new categories of spectra. In order to make use of all of the standard tools from homotopy theory, it is important to have a Quillen model category structure [##] available here. In this paper we provide a general method for lifting model structures to categories of rings, algebras, and modules. This includes, but is not limited to, each of the new theories of ring spectra. One model for structured ring spectra is given by the S-algebras of [##]. This example has the special feature that every object is brant, which makes it easier to fo...
