Fiore, Thomas M. and Pieper, Malte (2019) Waldhausen Additivity: classical and quasicategorical. JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 14 (1). pp. 109-197. ISSN 2193-8407, 1512-2891
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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 paper is dedicated to transferring these proofs to the quasicategorical setting and developing Waldhausen quasicategories and their sequences. We also give sufficient conditions for a split exact sequence to be equivalent to a standard one. These conditions are always satisfied by stable quasicategories, so Waldhausen K-theory sends any split exact sequence of pointed stable quasicategories to a split cofiber sequence. Presentability is not needed. In an effort to make the article self-contained, we recall all the necessary results from the theory of quasicategories, and prove a few quasicategorical results that are not in the literature.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ALGEBRAIC K-THEORY; QUASI-CATEGORIES; THEOREM; THOMASON; Waldhausen K-theory; Additivity; Quasicategory; Joyal model structure; Natural pushout functor |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Niko Naumann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 21 Apr 2020 10:01 |
| Last Modified: | 21 Apr 2020 10:01 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27493 |
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