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Let $R$ be an Artin algebra and $e$ an idempotent of $R$. Assume that ${\rmTor}_i^{eRe}(Re,G)=0$ for any $G\in{\rm GProj} eRe$ and $i$ sufficiently large.Necessary and sufficient conditions are given for the Schur functor $S_e$ toinduce a triangle-equivalence $\mathbb{D}_{def}(R)\simeq\mathbb{D}_{def}(eRe)$.Combine this with a result of Psaroudakis-Skartsaterhagen-Solberg [29], weprovide necessary and sufficient conditions for the singular equivalence$\mathbb{D}_{sg}(R)\simeq\mathbb{D}_{sg}(eRe)$ to restrict to atriangle-equivalence $\underline{{\rm GProj} R}\simeq\underline{{\rm GProj}eRe}$. Applying these to the triangular matrix algebra $T=\left(  \begin{array}{cc}  A & M \quad  0 & B  \end{array}  \right)$, corresponding results between candidate categories of $T$ and $A$(resp. $B$) are obtained. As a consequence, we infer Gorensteinness andCM-freeness of $T$ from those of $A$ (resp. $B$). Some concrete examples aregiven to indicate one can realise the Gorenstein defect category of atriangular matrix algebra as the singularity category of one of its corneralgabras.

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