On the algebraic K-theory of higher categories

Autor:	Barwick, C.
Rok vydání:	2012
Předmět:	Mathematics - K-Theory and Homology Mathematics - Algebraic Topology Mathematics - Category Theory
Druh dokumentu:	Working Paper
DOI:	10.1112/jtopol/jtv042
Popis:	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. Comment: 107 pages. Numerous corrections, thanks to an exceptional referee. Final preprint version; accepted at the Journal of Topology
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1204.3607 Zobrazit plný text záznamu View this record from Arxiv