On the algebraic K-theory of higher categories

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Abstract

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 simple universal property. Using this, we give new, higher categorical proofs of the Approximation, Additivity, and Fibration Theorems of Waldhausen in this context. As applications of this technology, we study the algebraic K-theory of associative rings in a wide range of homotopical contexts and of spectral Deligne-Mumford stacks.
Original languageEnglish
Pages (from-to)245-347
Number of pages107
JournalJournal of Topology
Volume9
Issue number1
Early online date11 Jan 2016
DOIs
Publication statusPublished - Mar 2016

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