## Stable Homotopy of Algebraic Theories (2001)

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Venue: | Topology |

Citations: | 11 - 1 self |

### BibTeX

@ARTICLE{Schwede01stablehomotopy,

author = {Stefan Schwede},

title = {Stable Homotopy of Algebraic Theories},

journal = {Topology},

year = {2001},

volume = {40},

pages = {1--41}

}

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### Abstract

The simplicial objects in an algebraic category admit an abstract homotopy theory via a Quillen model category structure. We show that the associated stable homotopy theory is completely determined by a ring spectrum functorially associated with the algebraic theory. For several familiar algebraic theories we can identify the parameterizing ring spectrum; for other theories we obtain new examples of ring spectra. For the theory of commutative algebras we obtain a ring spectrum which is related to AndreH}Quillen homology via certain spectral sequences. We show that the (co-)homology of an algebraic theory is isomorphic to the topological Hochschild (co-)homology of the parameterizing ring spectrum. # 2000 Elsevier Science Ltd. All rights reserved. MSC: 55U35; 18C10 Keywords: Algebraic theories; Ring spectra; AndreH}Quillen homology; #-spaces The original motivation for this paper came from the attempt to generalize a rational result about the homotopy theory of commutative rings. For...