On the algebraic K-theory of higher categories
Name
Barwick_On the algebraic.pdf
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876 KB
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Author(s)
Barwick, Clark Edward
Date Issued
January 2016
Journal
Journal of Topology
Publisher
Oxford University Press - London Mathematical Society
Citation
Barwick, Clark. “On the algebraicK-Theory of Higher Categories.” J Topology 9, no. 1 (January 12, 2016): 245–347.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1112/jtopol/jtv042
