2012/04/30 by C. Barwick · 1 citation
Mathematics · #math.KT #math.AT #math.CT
paper · pdf · doi:10.1112/jtopol/jtv042
107 pages. Numerous corrections, thanks to an exceptional referee. Final preprint version; accepted at the Journal of Topology
arxiv created 2015/11/06 · arxiv updated 2017/05/17
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.