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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.22186 |
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| _version_ | 1866910161906434048 |
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| author | Zhang, Chencheng Lu, Xue-Song Zhang, Pu |
| author_facet | Zhang, Chencheng Lu, Xue-Song Zhang, Pu |
| contents | Homotopic morphisms of $\mathbb E$-triangles in extriangulated categories are introduced. Any morphism of $\mathbb E$-triangles is a composition of homotopic morphisms. Any morphism $(α_1, α_2, α_3)$ of $\mathbb E$-triangles can be modified to be homotopic, by changing one of $α_i$; moreover, all the 15 cases where $α_i$ is an $\mathbb E$-inflation ($\mathbb E$-deflation) are analyzed. Some diagram theorems, especially $4\times 4$ Lemma and its $14$ variants, including $3\times 3$ diagram and Horseshoe Lemma, are investigated. A relation between homotopic morphisms and (middling) good morphisms in triangulated categories are given. Weakly idempotent complete extriangulated categories are characterized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homotopic morphisms and diagram theorems in extriangulated categories Zhang, Chencheng Lu, Xue-Song Zhang, Pu Category Theory Homotopic morphisms of $\mathbb E$-triangles in extriangulated categories are introduced. Any morphism of $\mathbb E$-triangles is a composition of homotopic morphisms. Any morphism $(α_1, α_2, α_3)$ of $\mathbb E$-triangles can be modified to be homotopic, by changing one of $α_i$; moreover, all the 15 cases where $α_i$ is an $\mathbb E$-inflation ($\mathbb E$-deflation) are analyzed. Some diagram theorems, especially $4\times 4$ Lemma and its $14$ variants, including $3\times 3$ diagram and Horseshoe Lemma, are investigated. A relation between homotopic morphisms and (middling) good morphisms in triangulated categories are given. Weakly idempotent complete extriangulated categories are characterized. |
| title | Homotopic morphisms and diagram theorems in extriangulated categories |
| topic | Category Theory |
| url | https://arxiv.org/abs/2604.22186 |