On the algebraic K-theory of higher categories
K-Theory and Homology
2017-05-17 v6 Algebraic Topology
Category Theory
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.
Keywords
Cite
@article{arxiv.1204.3607,
title = {On the algebraic K-theory of higher categories},
author = {C. Barwick},
journal= {arXiv preprint arXiv:1204.3607},
year = {2017}
}
Comments
107 pages. Numerous corrections, thanks to an exceptional referee. Final preprint version; accepted at the Journal of Topology