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arXiv · 2601.07352

Homotopy categories of admissible model structures on extriangulated categories

Shun-Jie Li·Yang Gao·Pu Zhang
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Abstract

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 $\Delta$ of distinguished triangles in the present paper and the class $\widetilde{\Delta}$ of distinguished triangles in \cite{NP} have the relation $\Delta = - \widetilde{\Delta}$, and hence the two triangulated structures on the homotopy category are isomorphic.

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Shun-Jie Li, Yang Gao, Pu Zhang. 2026-01-12. Homotopy categories of admissible model structures on extriangulated categories. https://arxiv.org/abs/2601.07352

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