Enriched model categories and an application to additive endomorphism spectra

Details Enriched model categories and an application to additive endomorphism spectra Enriched model categories and an application to additive endomorphism spectra

2006-02-06

arxiv.org/abs/math/0602107v2

Mathematics

Algebraic Topology

Sections completely re-organized from previous version. Mathematical content all the same

Scientific paper

We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in such a model category has a naturally associated endomorphism ring inside this spectra category. We establish the basic properties of this enrichment. We also develop some enriched model category theory. In particular, we have a notion of an adjoint pair of functors being a 'module' over another such pair. Such things are called "adjoint modules". We develop the general theory of these, and use them to prove a result about transporting enrichments over one symmetric monoidal model category to a Quillen equivalent one.

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