Geodesic
On matrix Toda brackets in Baues–Wirsching cohomology
Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 315-339.

Voir la notice de l'article provenant de la source International Press of Boston

Hardie, Kamps and Marcum have considered the matrix Toda brackets introduced by Barratt in the category of topological spaces from a $2$-categorical point of view. Baues and Dreckmann have shown that a class in the third Baues–Wirsching cohomology of a small category $\mathcal{C}$ governs every classical Toda bracket if the bracket is defined with a Toda category in $\mathcal{C}$. Our aim is to generalize such a relationship to that between the class in the cohomology and matrix Toda brackets in a $2$-category. Moreover, the non-triviality of the third cohomology is discussed via computation of a matrix Toda bracket in the category of cochain complexes on an additive category.
DOI : 10.4310/HHA.2018.v20.n2.a16
Classification : 18D05, 18E30, 55U35
Keywords: track category, linear track extension, universal Toda bracket, triangulated category 
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Yasuhiro Momose; Kenichirou Shinkai. On matrix Toda brackets in Baues–Wirsching cohomology. Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 315-339. doi : 10.4310/HHA.2018.v20.n2.a16. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n2.a16/

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