Enriched model categories and an application to additive endomorphism spectra

Daniel Dugger; Brooke Shipley

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arXiv · math/0602107

Enriched model categories and an application to additive endomorphism spectra

Daniel Dugger·Brooke Shipley

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Abstract

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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Daniel Dugger, Brooke Shipley. 2007-01-15. Enriched model categories and an application to additive endomorphism spectra. https://arxiv.org/abs/math/0602107

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