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Waldhausen Additivity: classical and quasicategorical

Fiore, Thomas M. ; Pieper, Malte


We use a simplicial product version of Quillen's Theorem A to prove classical Waldhausen Additivity of wS., which says that the subobject and quotient functors of cofiber sequences induce a weak equivalence wS.E(A,C,B)wS.AxwS.B. A consequence is Additivity for the Waldhausen K-theory spectrum of the associated split exact sequence, namely a stable equivalence of spectra K(A)K(B)K(E(A,C,B)). This ...


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