The Left and Right Triangulated Structures of Stable Categories

Abstract

Beligiannis and Marmaridis in 1994, constructed the one-sided triangulated structures on the stable categories of additive categories induced from some homologically finite subcategories. We extend their results to slightly more general settings. As an application of our results, we give some new examples of one-sided triangulated categories arising from abelian model categories. An interesting outcome is that we can describe the pretriangulated structures of the homotopy categories of abelian model categories via those of stable categories.

Key Words:

• Abelian model category
• Left triangulated category
• Pretriangulated category
• Stable category

2010 Mathematics Subject Classification:

• Primary: 18E30, 18G25
• Secondary: 55U35

ACKNOWLEDGMENTS

The author is indebted to Dr. Andrew Hubery for preparing the final version of this manuscript. The author would like to thank Prof. Xiao-Wu Chen, Guodong Zhou, and Xiaojin Zhang for helpful discussions. He would like to thank the anonymous referee for his/her helpful comments.

Notes

Communicated by D. Zacharia.