# Symmetric spectra

@inproceedings{Hovey1998SymmetricS, title={Symmetric spectra}, author={Mark Hovey and Brooke E. Shipley and Jeff Smith}, year={1998} }

Introduction 2 1. Symmetric spectra 5 1.1. Simplicial sets 5 1.2. Symmetric spectra 6 1.3. Simplicial structure on Sp 8 1.4. Symmetric Ω-spectra 10 2. The smash product of symmetric spectra 11 2.1. Symmetric sequences 11 2.2. Symmetric spectra 14 2.3. The ordinary category of spectra 18 3. Stable homotopy theory of symmetric spectra 19 3.1. Stable equivalence 20 3.2. Model categories 26 3.3. Level structure 32 3.4. Stable model category 34 4. Comparison with the Bousfield-Friedlander category…

## 630 Citations

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Symmetric spectra were introduced by Jeff Smith as a symmetric monoidal category of spectra. In this paper, a detection functor is defined which detects stable equivalences of symmetric spectra. This…

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### Symmetric ring spectra and topological Hochschild homology

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Symmetric spectra were introduced by Jeff Smith as a symmetric monoidal category of spectra. In this paper, a detection functor is defined which detects stable equivalences of symmetric spectra. This…

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Preface Pt. I: S.P. Novikov's Work on Operations on Complex Cobordism 2: Cobordism groups 3: Homology 4: The Conner-Floyd Chern classes 5: The Novikov operations 6: The algebra of all operations 7:…

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In recent years the theory of structured ring spectra (formerly known as A∞‐ and E∞‐ring spectra) has been simplified by the discovery of categories of spectra with strictly associative and…

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A functor is defined which detects stable equivalences of symmetric spectra. As an application, the definition of topological Hochschild homology on symmetric ring spectra using the Hochschild…

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A monoidal model category is a model category with a compatible closed monoidal structure. Such things abound in nature; simplicial sets and chain complexes of abelian groups are examples. Given a…

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In the appendix to [20] Waldhausen discussed a trace map tr:K(R)→HH(R), from the algebraic K‐theory of a ring to its Hochschild homology, which can be used to obtain information about K(R) from…

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