On the algebraic K-theory of higher categories
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, hi...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Oxford University Press - London Mathematical Society
2017
|
| Online Access: | http://hdl.handle.net/1721.1/110187 |
| _version_ | 1826187998501273600 |
|---|---|
| author | Barwick, Clark Edward |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Barwick, Clark Edward |
| author_sort | Barwick, Clark Edward |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T07:53:02Z |
| format | Article |
| id | mit-1721.1/110187 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:53:02Z |
| publishDate | 2017 |
| publisher | Oxford University Press - London Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/1101872022-09-23T09:23:22Z On the algebraic K-theory of higher categories Barwick, Clark Edward Massachusetts Institute of Technology. Department of Mathematics Barwick, Clark Edward 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. 2017-06-22T22:30:11Z 2017-06-22T22:30:11Z 2016-01 Article http://purl.org/eprint/type/JournalArticle 1753-8416 1753-8424 http://hdl.handle.net/1721.1/110187 Barwick, Clark. “On the algebraicK-Theory of Higher Categories.” J Topology 9, no. 1 (January 12, 2016): 245–347. en_US http://dx.doi.org/10.1112/jtopol/jtv042 Journal of Topology Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press - London Mathematical Society MIT web domain |
| spellingShingle | Barwick, Clark Edward On the algebraic K-theory of higher categories |
| title | On the algebraic K-theory of higher categories |
| title_full | On the algebraic K-theory of higher categories |
| title_fullStr | On the algebraic K-theory of higher categories |
| title_full_unstemmed | On the algebraic K-theory of higher categories |
| title_short | On the algebraic K-theory of higher categories |
| title_sort | on the algebraic k theory of higher categories |
| url | http://hdl.handle.net/1721.1/110187 |
| work_keys_str_mv | AT barwickclarkedward onthealgebraicktheoryofhighercategories |