Virtual operad algebras and realization of homotopy types

Research output: Contribution to journalArticlepeer-review


We prove that the category of algebras over a cofibrant operad admits a closed model category structure. This leads to the notion of "virtual operad algebra" - the algebra over a cofibrant resolution of the given operad. In particular, virtual commutative algebras can serve to an algebraic description of homotopy p-types as in the recent preprint of Mandell (M. Mandell, E-algebras and p-adic homotopy theory, Hopf preprint server, October, 1998). Our main result allows one to simplify the proof of Mandell's theorem.

Original languageEnglish
Pages (from-to)173-185
Number of pages13
JournalJournal of Pure and Applied Algebra
Issue number2-3
StatePublished - 24 May 2001


  • 18G55
  • 55P99

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Virtual operad algebras and realization of homotopy types'. Together they form a unique fingerprint.

Cite this