Cartan-Eilenberg complexes and Auslander categories
arXiv:1408.6728
Abstract
Let be a commutative noetherian ring with a semi-dualizing module . The Auslander categories with respect to are related through Foxby equivalence: $\xymatrix@C=50pt{\mathcal {A}_C(R) \ar@<0.4ex>[r]^{C\otimes^{\mathbf{L}}_{R} -} & \mathcal {B}_C(R) \ar@<0.4ex>[l]^{\mathbf{R}\mathrm{Hom}_{R}(C, -)}}$. We firstly intend to extend the Foxby equivalence to Cartan-Eilenberg complexes. To this end, C-E Auslander categories, C-E complexes and C-E -Gorenstein complexes are introduced, where denotes a self-orthogonal class of -modules. Moreover, criteria for finiteness of C-E Gorenstein dimensions of complexes in terms of resolution-free characterizations are considered.
19 pages. Comments and suggestions are appreciated