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Virtual operad algebras and realization of homotopy types

✍ Scribed by Vladimir Hinich

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 121 KB
Volume: 159
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(00)00054-2

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✦ Synopsis

We prove that the category of algebras over a coÿbrant operad admits a closed model category structure. This leads to the notion of "virtual operad algebra" -the algebra over a coÿbrant 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.

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