On exact ∞-categories and the Theorem of the Heart

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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 K-theory and Neeman K-theory. Additionally, it provides a new proof of the Devissage 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.
Original languageEnglish
Pages (from-to)2160-2186
Number of pages27
JournalCompositio Mathematica
Volume151
Issue number11
Early online date19 Aug 2015
DOIs
Publication statusPublished - Nov 2015

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