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A categorical approach to matrix Toda brackets

Authors: K. A. Hardie, K. H. Kamps and H. J. Marcum
Journal: Trans. Amer. Math. Soc. 347 (1995), 4625-4649
MSC: Primary 55U35; Secondary 18D05, 55Q35
MathSciNet review: 1303119
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Abstract: In this paper we give a categorical treatment of matrix Toda brackets, both in the pre- and post-compositional versions. Explicitly the setting in which we work is, à la Gabriel-Zisman, a $ 2$-category with zeros. The development parallels that in the topological setting but with homotopy groups replaced by nullity groups of invertible $ 2$-morphisms. A central notion is that of conjugation of $ 2$-morphisms. Our treatment of matrix Toda brackets is carried forward to the point of establishing appropriate indeterminacies.

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Article copyright: © Copyright 1995 American Mathematical Society