Enriched functors and stable homotopy theory

By Bjørn Ian Dundas, O. Rondigs, P. Østvær. Documenta Mathematica, 2003

58 citations recorded by the source corpus.

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 simpli- cial 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

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/00f57fcd8a9ab22366cfb22c4604f18a06f472ab

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In Algebra and Number Theory

1. G. Garkusha
2. Ivan Panin
3. M. Schlichting
4. M. Levine

In Geometry and Topology

1. G. Garkusha
2. Ivan Panin
3. M. Levine
4. M. Schlichting

In Mathematical Physics

1. G. Garkusha
2. Ivan Panin
3. M. Schlichting

Citations in the corpus

• Framed motives of algebraic varieties (after V. Voevodsky) (2014, background): “An advantage of these model structures is that a filtered colimit of fibrant objects is again fibrant [13, 5.3, 6.7] (in fact, both model structures are weakly finitely generated in the sense of [4]).”