2020 Volume 43 Issue 3 Pages 431-453
Let 
be an abelian category with enough projective objects and 
an additive and full subcategory of , and let 
be the Gorenstein category of . We study the properties of the -derived category 
, -singularity category 
and -defect category 
of . Let be admissible in . We show that 
if and only if 
; and 
if and only if the stable category 
of is triangle-equivalent to , and if and only if every object in has finite -proper -dimension. Then we apply these results to module categories. We prove that under some condition, the Gorenstein derived equivalence of artin algebras induces the Gorenstein singularity equivalence. Finally, for an artin algebra A, we establish the stability of Gorenstein defect categories of A.
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