On exact ∞-categories and the Theorem of the Heart

Abstract

The new homotopy theory of exact∞-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 KK-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.