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Hom_{\\mathbf{DM}^\\mathrm{GW}_\\mathrm{eff}}(A^\\bullet(1),B^\\bullet(1)),$$ for $A^\\bullet,B^\\bullet\\in \\mathbf{DM}^\\mathrm{GW}_\\mathrm{eff}(k)$ in the category of effective Grothendieck-Witt-motives constructed in \\cite{AD_DMGWeff} is obtained (and similarly for Witt-motives).\n  This implies that the canonical functor 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