Triple brackets and lax morphism categories
The theory of secondary operations in homotopy groups has been extended to the context of a \(2\)-category \({\mathcal C}\) with zeros. In this paper the authors study the lax morphism category \(m{\mathcal C}\), thereby generalising operations in relative homotopy groups. In particular they study Toda brackets in \(m{\mathcal C}\). They consider the behaviour of these brackets when \({\mathcal C}\) has a suspension functor, and they apply their results to homotopy groups of spheres. They also describe two-sided matrix Toda brackets, which are applied to homotopy groups of spheres and to quaternary Toda brackets.
scientific article; zbMATH DE number 2069037