New York Journal of Mathematics
Volume 26 (2020), 37-91


Bertrand J. Guillou and J. Peter May

Enriched model categories and presheaf categories

view    print

Published: January 1, 2020.
Keywords: Enriched model categories, enriched presheaf categories.
Subject: 55U35, 55P42.

We collect in one place a variety of known and folklore results in enriched model category theory and add a few new twists. The central theme is a general procedure for constructing a Quillen adjunction, often a Quillen equivalence, between a given V-model category and a category of enriched presheaves in V, where V is any good enriching category. For example, we rederive the result of Schwede and Shipley that reasonable stable model categories are Quillen equivalent to presheaf categories of spectra (alias categories of module spectra) under more general hypotheses. The technical improvements and modifications of general model categorical results given here are applied to equivariant contexts in the sequels [13, 14], where we indicate various directions of application.


It is a pleasure to thank an anonymous referee for an especially helpful report. This work was partially supported by Simons Collaboration Grant No. 282316 held by the first author.

Author information

Bertrand J. Guillou:
Department of Mathematics
University of Kentucky
Lexington, KY 40506, USA


J. Peter May:
Department of Mathematics
The University of Chicago
Chicago, IL 60637, USA