Resolution of coloured operads and rectification of homotopy algebras

Details Resolution of coloured operads and rectification of homotopy algebras Resolution of coloured operads and rectification of homotopy algebras

2005-12-26

arxiv.org/abs/math/0512576v2

Contemp. Math. 431 (2007) 31-58

Mathematics

Algebraic Topology

published version

Scientific paper

We 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.

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