Higher order Toda brackets (Q2230809)

The author describes two ways to define higher order Toda brackets in a pointed simplicial model category \(\mathcal{D}\): one is a recursive definition using model categorical constructions, and the second uses the associated simplicial enrichment. He shows that these two definitions agree, by providing a third, diagrammatic, description of the Toda bracket, and explains how it serves as the obstruction to rectifying a certain homotopy-commutative diagram in \(\mathcal{D}\).