Symmetric Auslander and Bass categories
Symmetric Auslander and Bass categories
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DOI：
10.1017/s0305004110000629
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发表时间：
2010-01
影响因子：
0.8
通讯作者：
Peter Jørgensen;Kiriko Kato
中科院分区：
文献类型：
--
作者：
Peter Jørgensen;Kiriko Kato
本文定义对称Auslander范畴As（R）由投射模复形组成，其左尾和右尾等于投射模的全无圈复形的左尾和右尾。对称Auslander范畴包含A（R），普通Auslander范畴。众所周知，A（R）与Gorenstein投射模密切相关，我们的主要结果是，A（R）与可以合理地称为Gorenstein投射同态的映射类似地相关。也就是说，存在三角范畴\[ \underline{\G莫尔}（R）\stackrel{\simeq}{\rightarrow} \sA^{\s}（R）/ \sK^{\bounded}（\Prj\，R）\]的等价性，其中G莫尔（R）是R-模同态的交换范畴莫尔（R）中Gorenstein投射对象的稳定范畴。这一结果是设置在更广泛的背景下的理论为As（R）和Bs（R），对称巴斯范畴，这是双重定义。
Abstract We define the symmetric Auslander category As(R) to consist of complexes of projective modules whose left- and right-tails are equal to the left- and right-tails of totally acyclic complexes of projective modules. The symmetric Auslander category contains A(R), the ordinary Auslander category. It is well known that A(R) is intimately related to Gorenstein projective modules, and our main result is that As(R) is similarly related to what can reasonably be called Gorenstein projective homomorphisms. Namely, there is an equivalence of triangulated categories \[ \underline{\GMor}(R) \stackrel{\simeq}{\rightarrow} \sA^{\s}(R) / \sK^{\bounded}(\Prj\,R) \] where GMor(R) is the stable category of Gorenstein projective objects in the abelian category Mor(R) of homomorphisms of R-modules. This result is set in the wider context of a theory for As(R) and Bs(R), the symmetric Bass category which is defined dually.