Stable homotopy of algebraic theories

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 Andre-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. (C) 2000 Elsevier Science Ltd. All rights reserved.