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THE HOMOTOPY CATEGORIES OF N-COMPLEXES OF INJECTIVES AND PROJECTIVES
Xie, Zongyang,Yang, Xiaoyan Korean Mathematical Society 2019 대한수학회지 Vol.56 No.3
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.
The homotopy categories of $N$-complexes of injectives and projectives
Zongyang Xie,Xiaoyan Yang 대한수학회 2019 대한수학회지 Vol.56 No.3
We investigate the homotopy category $\mathcal{K}_N(\mathrm{Inj}\mathscr{A})$ of $N$-comp\-lexes of injectives in a Grothendieck abelian category $\mathscr{A}$ not necessarily locally noetherian, and prove that the inclusion $\mathcal{K}(\mathrm{Inj}\mathscr{A})\rightarrow\mathcal{K}(\mathscr{A})$ has a left adjoint and $\mathcal{K}_N(\mathrm{Inj}\mathscr{A})$ is well generated. We also show that the homotopy category $\mathcal{K}_N(\mathrm{Prj}R)$ of $N$-complexes of projectives is compactly generated whenever $R$ is right coherent.