Abstract
We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category F such that the homotopy category of this model structure is equivalent to the stable category 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 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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This project was partly supported by National Natural Science Foundation of China (Nos. 11671174 and 11571329).
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Li, ZW. A note on model structures on arbitrary Frobenius categories. Czech Math J 67, 329–337 (2017). https://doi.org/10.21136/CMJ.2017.0582-15
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DOI: https://doi.org/10.21136/CMJ.2017.0582-15