Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866914920906358784 |
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| author | Shah, Amit |
| author_facet | Shah, Amit |
| contents | We generalise some of the theory developed for abelian categories in papers of Auslander and Reiten to semi-abelian and quasi-abelian categories. In addition, we generalise some Auslander-Reiten theory results of S. Liu for Krull-Schmidt categories by removing the Hom-finite and indecomposability restrictions. Finally, we give equivalent characterisations of Auslander-Reiten sequences in a quasi-abelian, Krull-Schmidt category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_11043 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories Shah, Amit Category Theory Representation Theory 18E05 (Primary) 18E10, 18E40 (Secondary) We generalise some of the theory developed for abelian categories in papers of Auslander and Reiten to semi-abelian and quasi-abelian categories. In addition, we generalise some Auslander-Reiten theory results of S. Liu for Krull-Schmidt categories by removing the Hom-finite and indecomposability restrictions. Finally, we give equivalent characterisations of Auslander-Reiten sequences in a quasi-abelian, Krull-Schmidt category. |
| title | Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories |
| topic | Category Theory Representation Theory 18E05 (Primary) 18E10, 18E40 (Secondary) |
| url | https://arxiv.org/abs/1809.11043 |