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On exact $\infty$ -categories and the Theorem of the Heart

  • Clark Barwick (a1)
Abstract

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.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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