When the Schur functor induces a triangle-equivalence between Gorenstein defect categories

Let R be an Artin algebra and e idempotent of R. Assume that Tor (Re, G) = 0 for any G ∈ Gproj eRe i sufficiently large. Necessary sufficient conditions are given the Schur functor Se to induce a triangle-equivalence ⅅdef(R) ≃ ⅅdef(eRe). Combining this with result Psaroudakis et al. (2014), we provide necessary singular equivalence ⅅsg(R) ⅅsg(eRe) restrict GprojR GprojeRe. Applying these triangular matrix $$T \left( {\matrix{A & M \cr B } \right)$$ , corresponding results between candidate categories T A (resp. B) obtained. As consequence, infer Gorensteinness CM (Cohen-Macaulay)-freeness from those B). Some concrete examples indicate one can realise Gorenstein defect category as singularity its corner algebras.