On exact categories and their stable envelopes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912733236035584 |
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| author | Saunier, Victor Winges, Christoph |
| author_facet | Saunier, Victor Winges, Christoph |
| contents | We show that Klemenc's stable envelope of exact $\infty$-categories induces an equivalence between stable $\infty$-categories with a bounded heart structure and weakly idempotent complete exact $\infty$-categories. Moreover, we generalise the Gillet-Waldhausen theorem to the connective algebraic K-theory of exact $\infty$-categories and deduce a universal property of connective algebraic K-theory as an additive invariant on exact $\infty$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03408 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On exact categories and their stable envelopes Saunier, Victor Winges, Christoph K-Theory and Homology Algebraic Topology Category Theory We show that Klemenc's stable envelope of exact $\infty$-categories induces an equivalence between stable $\infty$-categories with a bounded heart structure and weakly idempotent complete exact $\infty$-categories. Moreover, we generalise the Gillet-Waldhausen theorem to the connective algebraic K-theory of exact $\infty$-categories and deduce a universal property of connective algebraic K-theory as an additive invariant on exact $\infty$-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. |
| title | On exact categories and their stable envelopes |
| topic | K-Theory and Homology Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2502.03408 |