Chain complexes and stable categories
Chain complexes and stable categories
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DOI：
10.1007/bf02568439
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发表时间：
1990-12
影响因子：
0.6
通讯作者：
B. Keller
中科院分区：
文献类型：
--
作者：
B. Keller
在适当的假设下，我们将加法子范畴$$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{X}}\子集\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{A}}$$(=具有足够内射的精确范畴的稳定范畴)的包含推广到ANS-Functor[15]$$\Mathcal{H}_{0]}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\Mathcal{X}}\to\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{A}}$$，式中，$$\Mathcal{H}_{0]}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{X}}$$是链复合体的正度集中的同伦范畴。从而对J.Rickard[17]的“Morita派生范畴理论”[17]的主要结果得到了新的证明，并对Happl[12，10.10]关于有限维代数派生范畴的“模论描述”的一个定理进行了加强。
Under suitable assumptions, we extend the inclusion of an additive subcategory $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{X}} \subset \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{A}}$$ (=stable category of an exact category with enough injectives) to anS-functor [15] $$\mathcal{H}_{0]} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{X}} \to \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{A}}$$ , where $$\mathcal{H}_{0]} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\mathcal{X}}$$ is the homotopy category of chain complexes concentrated in positive degrees. We thereby obtain a new proof for the key result of J. Rickard’s ‘Morita theory for Derived categories’ [17] and a sharpening of a theorem of Happel [12,10.10] on the ‘module-theoretic description’ of the derived category of a finite-dimensional algebra.