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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

##### MSC:
 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