On the Toda bracket understood via homotopy-coherent pasting diagrams in the homotopy 2-category of pointed topological spaces:
Keith Hardie, Howard Marcum, Nobuyuki Oda, Bracket operations in the homotopy theory of a 2-category, Rend. Ist. Mat. Univ. Trieste 33, 19–70 (2001) (rendiconti:33/02)
Keith Hardie, Klaus Heiner Kamps, Howard Marcum, The Toda bracket in the homotopy category of a track bicategory, Journal of Pure and Applied Algebra Volume 175, Issues 1–3, 8 November 2002, Pages 109-133 (doi:10.1016/S0022-4049(02)00131-7)
Howard Marcum, Nobuyuki Oda, Long Box Bracket Operations in Homotopy Theory, Appl Categor Struct 19, 137–173 (doi:10.1007/s10485-009-9186-3)
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