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This gives a construction that extends any given dg functor $F : A \\rightarrow B$ between smooth dg categories to a dg functor $\\widetilde{F} : \\widetilde{A} \\rightarrow \\widetilde{B}$, together with a family of deformations of $(\\widetilde{A},\\widetilde{B},\\widetilde{F})$ parametrized by relative negative cyclic homology classes $\\widetilde{\\eta} \\in HN_{n-2}(B, A)$. We prove that these extensions admit relative $n$-Calabi-Yau structures in the sense of \\cite{BD19}. 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This gives a construction that extends any given dg functor $F : A \\rightarrow B$ between smooth dg categories to a dg functor $\\widetilde{F} : \\widetilde{A} \\rightarrow \\widetilde{B}$, together with a family of deformations of $(\\widetilde{A},\\widetilde{B},\\widetilde{F})$ parametrized by relative negative cyclic homology classes $\\widetilde{\\eta} \\in HN_{n-2}(B, A)$. We prove that these extensions admit relative $n$-Calabi-Yau structures in the sense of \\cite{BD19}. 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