Enriched Functors and Stable Homotopy Theory

In this paper we employ enriched category theory to construct a convenient model for several stable homotopy categories. This is achieved in a three-step process by introducing the pointwise, homotopy functor and stable model category structures for enriched functors. The general setup is shown to describe equivariant stable homotopy theory, and we recover Lydakis' model category of simplicial functors as a special case. Other examples -- including motivic homotopy theory -- will be treated in subsequent papers.

2000 Mathematics Subject Classification: 55P42, 55U35, 18D20, 55P91

Keywords and Phrases: model structures for enriched functor categories, stable homotopy theory, equivariant stable homotopy theory

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