On the algebraic K-theory of higher categories
Autor: | Barwick, C. |
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Rok vydání: | 2012 |
Předmět: | |
Druh dokumentu: | Working Paper |
DOI: | 10.1112/jtopol/jtv042 |
Popis: | We prove that Waldhausen K-theory, when extended to a very general class of quasicategories, can be described as a Goodwillie differential. In particular, K-theory spaces admit canonical (connective) deloopings, and the K-theory functor enjoys a universal property. Using this, we give new, higher categorical proofs of both the additivity and fibration theorems of Waldhausen. As applications of this technology, we study the algebraic K-theory of associative ring spectra and spectral Deligne-Mumford stacks. Comment: 107 pages. Numerous corrections, thanks to an exceptional referee. Final preprint version; accepted at the Journal of Topology |
Databáze: | arXiv |
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