Saunier, Victor and Winges, Christoph (2026) On exact categories and their stable envelopes. MATHEMATISCHE ZEITSCHRIFT, 312 (1): 28. ISSN 0025-5874, 1432-1823
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We show that Klemenc's stable envelope of exact infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\infty $$\end{document}-categories induces an equivalence between stable infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\infty $$\end{document}-categories with a bounded heart structure and weakly idempotent complete exact infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\infty $$\end{document}-categories. Moreover, we generalise the Gillet-Waldhausen theorem to the connective algebraic K-theory of exact infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\infty $$\end{document}-categories and deduce a universal property of connective algebraic K-theory as an additive invariant on exact infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\infty $$\end{document}-categories. A key tool is a generalisation of a theorem due to Keller which provides a sufficient condition for an exact functor to induce a fully faithful functor on stable envelopes.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NEGATIVE K-THEORY; THEOREM; Stable envelope; Gabriel-Quillen embedding; Heart structures; Gillet-Waldhausen theorem |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Jun 2026 07:51 |
| Last Modified: | 23 Jun 2026 07:51 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66396 |
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