15 research outputs found
Auslander-Buchweitz approximation theory for triangulated categories
We introduce and develop an analogous of the Auslander-Buchweitz
approximation theory (see \cite{AB}) in the context of triangulated categories,
by using a version of relative homology in this setting. We also prove several
results concerning relative homological algebra in a triangulated category
\T, which are based on the behavior of certain subcategories under finiteness
of resolutions and vanishing of Hom-spaces. For example: we establish the
existence of preenvelopes (and precovers) in certain triangulated subcategories
of \T. The results resemble various constructions and results of Auslander
and Buchweitz, and are concentrated in exploring the structure of a
triangulated category \T equipped with a pair (\X,\omega), where \X is
closed under extensions and is a weak-cogenerator in \X, usually
under additional conditions. This reduces, among other things, to the existence
of distinguished triangles enjoying special properties, and the behavior of
(suitably defined) (co)resolutions, projective or injective dimension of
objects of \T and the formation of orthogonal subcategories. Finally, some
relationships with the Rouquier's dimension in triangulated categories is
discussed.Comment: To appear at: Appl. Categor. Struct. (2011); 22 page
Strategies for Enhancing Phytonutrient Content in Plant-Based Foods
info:eu-repo/semantics/publishedVersio