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Keywords:
Frobenius categorie; triangulated categories; model structure
Frobenius categorie; triangulated categories; model structure
Summary:
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).
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