A note on model structures on arbitrary Frobenius categories

Czechoslovak Mathematical Journal

Zhi-Wei Li¹ 

关键词: Frobenius categorie;    triangulated categories;    model structure;   

DOI  :  10.21136/CMJ.2017.0582-15

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category $\mathcal{F}$ such that the homotopy category of this model structure is equivalent to the stable category $\underline{\mathcal{F}}$ as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When $\mathcal{F}$ is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact (closed) model structure in the sense of Gillespie (2011).

【 授权许可】

Unknown