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We show that the relative Auslander-Buchweitz context on a triangulated category $\T$ coincides with the notion of co--structure on certain triangulated subcategory of $\T$ (see Theorem \ref{M2}). In the Krull-Schmidt case, we stablish a bijective correspondence between co--structures and cosuspended, precovering subcategories (see Theorem \ref{correspond}). We also give a characterization of bounded co--structures in terms of relative homological algebra. The relationship between silting classes and co--structures is also studied. We prove that a silting class induces a bounded non-degenerated co--structure on the smallest thick triangulated subcategory of $\T$ containing We also give a description of the bounded co--structures on $\T$ (see Theorem \ref{Msc}). Finally, as an application to the particular case of the bounded derived category $\D(\HH),$ where $\HH$ is an abelian hereditary category which is Hom-finite, Ext-finite and has a tilting object (see \cite{HR}), we give a bijective correspondence between finite silting generator sets $\omega=\add\,(\omega)$ and bounded co--structures (see Theorem \ref{teoH}).