Admissibility and rectification of colored symmetric operads

Dmitry Pavlov, Jakob Scholbach

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We establish a highly flexible condition that guarantees that all colored symmetric operads in a symmetric monoidal model category are admissible, that is, the category of algebras over any operad admits a model structure transferred from the original model category. We also give a necessary and sufficient criterion that ensures that a given weak equivalence of admissible operads admits rectification, that is, the corresponding Quillen adjunction between the categories of algebras is a Quillen equivalence. In addition, we show that Quillen equivalences of underlying symmetric monoidal model categories yield Quillen equivalences of model categories of algebras over operads. Applications of these results include enriched categories, colored operads, prefactorization algebras, and commutative symmetric ring spectra.

Original languageEnglish
Pages (from-to)559-601
Number of pages43
JournalJournal of Topology
Issue number3
StatePublished - Jun 12 2018


  • 18D20 (secondary)
  • 18D50
  • 18G55
  • 55P43
  • 55P48
  • 55U35 (primary)


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