2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146107We provide general conditions under which the algebras for a coloured operad in a monoidal model category carry a Quillen model structure, and prove a Comparison Theorem to the effect that a weak equivalence between suitable such operads induces a Quillen equivalence between their categories of algebras. We construct an explicit Boardman-Vogt style cofibrant resolution for coloured operads, thereby giving a uniform approach to algebraic structures up to homotopy over coloured operads. The Comparison Theorem implies that such structures can be rectified.published versionAlgebraic Topology18D50 (Primary); 18G55, 55U35 (Secondary)text