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We define the depth relative to $T$ and the delooping level relative to $T$ and show that the finitistic dimension of the opposite algebra of $B$ is bounded by the depth of $\\textup{Fac}T$ relative to $T$ and the delooping level of $\\textup{Fac}T$ relative to $T$. We give applications to the finitistic dimension conjecture. 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Denote by ${\\rm Fac}T$ the subcategory of finitely generated right $A$-modules generated by $T$. We define the depth relative to $T$ and the delooping level relative to $T$ and show that the finitistic dimension of the opposite algebra of $B$ is bounded by the depth of $\\textup{Fac}T$ relative to $T$ and the delooping level of $\\textup{Fac}T$ relative to $T$. We give applications to the finitistic dimension conjecture. 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