On exact -categories and the Theorem of the Heart

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.