Erratum to "Homological algebra of homotopy algebras"

TL;DR

This paper corrects a previously claimed theorem about the existence of a model structure on operads by providing a counter-example and a revised statement.

Contribution

It identifies an error in a key theorem and offers a corrected version supported by a counter-example.

Findings

Counter-example disproves the original theorem

Provides a corrected version of the theorem

Clarifies conditions for model structures on operads

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.