2014/08/28 by Wei Ren, Ren, Wei, Zhongkui Liu +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1408.6728
openalex publication_date 2014/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a commutative noetherian ring with a semi-dualizing module C. The Auslander categories with respect to C are related through Foxby equivalence: \xymatrix@C=50pt\mathcal AC(R) \ar@<0.4ex>[r]^C⊗LR - & \mathcal BC(R) \ar@<0.4ex>[l]^RHomR(C, -). We firstly intend to extend the Foxby equivalence to Cartan-Eilenberg complexes. To this end, C-E Auslander categories, C-E W complexes and C-E W-Gorenstein complexes are introduced, where W denotes a self-orthogonal class of R-modules. Moreover, criteria for finiteness of C-E Gorenstein dimensions of complexes in terms of resolution-free characterizations are considered.