Geodesic
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).
DOI : 10.21136/CMJ.2017.0582-15
Classification : 18E10, 18E30, 18E35
Keywords: Frobenius categorie; triangulated categories; model structure 
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     title = {A note on model structures on arbitrary {Frobenius} categories},
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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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