On the algebraic K‐theory of higher categories
By Clark Barwick. 2012
123 citations recorded by the source corpus.
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 article. 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5e096ce88c3cb689f3b489087acd6cede1a99094
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Marc Hoyois
- Sarah Scherotzke
- Nicolò Sibilla
- Clark Barwick
- D. Gepner
- David White
- J. Pridham
- R. Haugseng
In Geometry and Topology
- Marc Hoyois
- Sarah Scherotzke
- Nicolò Sibilla
- Clark Barwick
- M. Levine
- D. Gepner
- David White
- J. Pridham
In Mathematical Physics
- Marc Hoyois
- Sarah Scherotzke
- Nicolò Sibilla
- Clark Barwick
- M. Levine
- D. Gepner
- David White
- J. Pridham
Citations in the corpus
- On exact $\infty$-categories and the Theorem of the Heart (2012, methodology): “This self-duality is then used in conjunction with our ∞ -categorical Fibration Theorem [3, Pr. 10.12] to prove the following.”
- Higher traces, noncommutative motives, and the categorified Chern character (2015, background): “5 is not a formal consequence of the universal property of K-theory [9,6].”