Homotopy Equivalences induced by Balanced Pairs
Homotopy Equivalences induced by Balanced Pairs
复制标题
DOI：
10.1016/j.jalgebra.2010.09.002
复制
发表时间：
2008-11
期刊：
影响因子：
--
通讯作者：
Xiao-Wu Chen
中科院分区：
文献类型：
--
作者：
Xiao-Wu Chen
我们在交换范畴中引入了加法子范畴的平衡对的概念。给出了两个同伦复形范畴之间的三角等价关系的充分条件。作为应用，我们证明了对于左Gorenstein环，其Gorenstein投射模的同伦范畴与Gorenstein内射模的同伦范畴之间存在三角等价，这限制了投射模的同伦范畴与内射模的同伦范畴之间的三角等价。在交换Gorenstein环的情况下，我们证明了直到自然同构，我们的等价推广了Iyengar-Krause的等价。
We introduce the notion of balanced pair of additive subcategories in an abelian category. We give sufficient conditions under which a balanced pair of subcategories gives rise to a triangle-equivalence between two homotopy categories of complexes. As an application, we prove that for a left-Gorenstein ring, there exists a triangle-equivalence between the homotopy category of its Gorenstein projective modules and the homotopy category of its Gorenstein injective modules, which restricts to a triangle-equivalence between the homotopy category of projective modules and the homotopy category of injective modules. In the case of commutative Gorenstein rings we prove that up to a natural isomorphism our equivalence extends Iyengar–Krause's equivalence.