Czechoslovak Mathematical Journal, online first, 9 pp.

A note on model structures on arbitrary Frobenius categories

Zhi-Wei Li

Received October 26, 2015.   First published March 1, 2017.

Zhi-Wei Li, School of Mathematics and Statistics, Jiangsu Normal University, 101 Shanghai Road, Xuzhou 221116, Jiangsu, P. R. China, e-mail: zhiweili@jsnu.edu.cn

Abstract: 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).

Keywords: Frobenius categorie; triangulated categories; model structure

Classification (MSC 2010): 18E10, 18E30, 18E35

DOI: 10.21136/CMJ.2017.0582-15

Full text available as PDF.


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