Enriched functors and stable homotopy theory
The paper establishes a very general framework to study structured ring spectra. It is suitable to describe equivariant stable homotopy theory and motivic homotopy theory, see \textit{V. Voevodsky} [Doc. Math., J. DMV, Extra Vol. ICM Berlin 1998, vol. I, 579--604 (1998; Zbl 0907.19002)]. Such frameworks are important since they make tools from algebra applicable to topology and vice versa. The starting point is a monoidal model category \(V\) and a finitely presentable cofibrant object \(T\) of \(V\) which plays the role of the sphere in topology. The main theorem says that there is a monoidal model category \(F\) which satisfies the monoid axiom and which is right Quillen equivalent to the stable model category of \(T\)-spectra in \(V\). An object of \(F\) is an enriched functor \(X\) from finitely presentable objects of \(V\) to \(V\). The equivalence is given by evaluating \(X\) on powers of \(T\). This point of view was first introduced by \textit{M. Lydakis}, [Simplicial functors and stable homotopy theory. Preprint 98-049, SFB 343, Bielefeld (1998)] for the category of simplicial sets.
structures for enriched functor categories
scientific article; zbMATH DE number 2028919