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A note on model structures on arbitrary Frobenius categories
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 329-337
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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).
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).
DOI : 10.21136/CMJ.2017.0582-15
Classification : 18E10, 18E30, 18E35
Keywords: Frobenius categorie; triangulated categories; model structure 
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Li, Zhi-wei. A note on model structures on arbitrary Frobenius categories. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 329-337. doi: 10.21136/CMJ.2017.0582-15

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