%0 Journal Article
%T Virtual operad algebras and realization of homotopy types
%A Vladimir Hinich
%J Mathematics
%D 1999
%I arXiv
%X 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-tipes as in the recent preprint of Mandell (electronic Hopf topology archive, october '98, see http://www.hopf.math.purdue.edu. Our main result allows one to significally simplify the proof of Mandell's theorem.
%U http://arxiv.org/abs/math/9907115v1