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Opérations de Massey, la construction S et extensions de Yoneda. (Massey operations, S-construction and Yoneda extension). (French) Zbl 0569.55012
For any category \({\mathcal C}\) with cofibrations a simplicial set S\({\mathcal C}\) is constructed called the Waldhausen S-construction of \({\mathcal C}\). Here are defined the obstructions for S\({\mathcal C}\) to be a Kan simplicial set. For Quillen exact categories [D. Quillen, Lect. Notes Math. 341, 85-147 (1973; Zbl 0292.18004)] these obstructions are finer invariants than K-functors. Furthermore, they are connected to Massey- Yoneda operations through the generalization of an Adams construction [J. F. Adams, Topology 5, 21-71 (1966; Zbl 0145.199)].
Reviewer: G.Hoff

55U35 Abstract and axiomatic homotopy theory in algebraic topology
55S30 Massey products
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
55U10 Simplicial sets and complexes in algebraic topology
18G30 Simplicial sets; simplicial objects in a category (MSC2010)
18E10 Abelian categories, Grothendieck categories