Erratum to "Homological algebra of homotopy algebras"

Abstract

Theorem 6.1.1 of [H.A.H.A.] on the existence of a model structure on the category of operads is not valid in the generality claimed. We present here a counter-example (due to B. Fresse) and a corrected version of the theorem.

5 pages; explained that the error discussed has no implications on the usage of cofibrant resolutions of operads (in particular, of the Eilenberg-Zilber operad). A remark on the paper of Berger-Moerdijk fixed

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• Formality of Sinha's cosimplicial model for long knots spaces and the Gerstenhaber algebra structure of homology
• Homotopy theory of modules over operads and non-Sigma operads in monoidal model categories
• Derived homotopy algebras
• Quotients of unital $A_{\infty }$-categories
• Homotopy theory of curved operads and curved algebras
• Complex manifolds as families of homotopy algebras
• Stabilizations of ${\mathbb{E}}_{\infty }$ Operads and $p$-Adic Stable Homotopy Theory
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies
• Up-to-homotopy algebras with strict units. (Extended abstract version.)