Enriched model categories and presheaf categories

Bertrand J. Guillou, J. Peter May

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 adjunc-tion, 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.

Original languageEnglish
Pages (from-to)37-91
Number of pages55
JournalNew York Journal of Mathematics
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020, University at Albany. All rights reserved.


  • Enriched model categories
  • Enriched presheaf categories

ASJC Scopus subject areas

  • General Mathematics


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