On exact $\infty$-categories and the Theorem of the Heart
By Clark Barwick. Compositio Mathematica, 2012
52 citations recorded by the source corpus.
The new homotopy theory of exact$\infty$-categories is introduced and employed to prove a Theorem of the Heart for algebraic $K$-theory (in the sense of Waldhausen). This implies a new compatibility between Waldhausen $K$-theory and Neeman $K$-theory. Additionally, it provides a new proof of the Dévissage and Localization theorems of Blumberg–Mandell, new models for the $G$-theory of schemes, and a proof of the invariance of $G$-theory under derived nil-thickenings.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ca3296dd296c695c3202a22e3f0fe03a5b47f98b
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In Algebra and Number Theory
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Citations in the corpus
- Spectral Mackey functors and equivariant algebraic K-theory, II (2015, methodology): “ents. I have had very helpful conversations with David Ayala and Haynes Miller about the contents of this paper and its sequels. 1. Preliminarieson∞-categories In general, we use the terminology from [25, 2, 1]. We review some of the relevant notation here. 1.1. Notation. In order to deal gracefully”
- The special fiber of the motivic deformation of the stable homotopy category is algebraic (2018, background): “[4] Barwick, C., On exact ∞-categories and the theorem of the heart.”