Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE HOMOTOPY CATEGORIES OF N-COMPLEXES OF INJECTIVES AND PROJECTIVES

  • Xie, Zongyang (Department of Mathematics Northwest Normal University) ;
  • Yang, Xiaoyan (Department of Mathematics Northwest Normal University)
  • Received : 2018.03.15
  • Accepted : 2018.06.01
  • Published : 2019.05.01
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Abstract

We investigate the homotopy category ${\mathcal{K}}_N(Inj{\mathfrak{A}})$ of N-complexes of injectives in a Grothendieck abelian category ${\mathfrak{A}}$ not necessarily locally noetherian, and prove that the inclusion ${\mathcal{K}}_N(Inj{\mathfrak{A}}){\rightarrow}{\mathcal{K}}({\mathfrak{A}})$ has a left adjoint and ${\mathcal{K}}_N(Inj{\mathfrak{A}})$ is well generated. We also show that the homotopy category ${\mathcal{K}}_N(PrjR)$ of N-complexes of projectives is compactly generated whenever R is right coherent.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

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