Homotopy categories of admissible model structures on extriangulated categories
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915723103698944 |
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| author | Li, Shun-Jie Gao, Yang Zhang, Pu |
| author_facet | Li, Shun-Jie Gao, Yang Zhang, Pu |
| contents | The extriangulated category is a simultaneous generalization of exact categories and triangulated categories. H. Nakaoka and Y. Palu have proved that the homotopy category of an admissible model structure on a weakly idempotent complete extriangulated category is a triangulated category. Using the classic construction of distinguished triangles given by A. Heller and D. Happel, this paper provides an alternative proof of Nakaoka - Palu Theorem. In fact, the class $Δ$ of distinguished triangles in the present paper and the class $\widetildeΔ$ of distinguished triangles in \cite{NP} have the relation $Δ= - \widetildeΔ$, and hence the two triangulated structures on the homotopy category are isomorphic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_07352 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homotopy categories of admissible model structures on extriangulated categories Li, Shun-Jie Gao, Yang Zhang, Pu Representation Theory The extriangulated category is a simultaneous generalization of exact categories and triangulated categories. H. Nakaoka and Y. Palu have proved that the homotopy category of an admissible model structure on a weakly idempotent complete extriangulated category is a triangulated category. Using the classic construction of distinguished triangles given by A. Heller and D. Happel, this paper provides an alternative proof of Nakaoka - Palu Theorem. In fact, the class $Δ$ of distinguished triangles in the present paper and the class $\widetildeΔ$ of distinguished triangles in \cite{NP} have the relation $Δ= - \widetildeΔ$, and hence the two triangulated structures on the homotopy category are isomorphic. |
| title | Homotopy categories of admissible model structures on extriangulated categories |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.07352 |