Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 329–337

A note on model structures on arbitrary Frobenius categories

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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).

Keywords

Frobenius categorie triangulated categories model structure 

MSC 2010

18E10 18E30 18E35 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhou, JiangsuP.R. China

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