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arXiv · 1204.3607

On the algebraic K-theory of higher categories

C. Barwick
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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 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.

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C. Barwick. 2012-04-16. On the algebraic K-theory of higher categories. https://doi.org/10.1112/jtopol/jtv042

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