The homological theory of contravariantly finite subcategories:auslander-buchweitz contexts, gorenstein categories and (co-)stabilization

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Proper classes and Gorensteinness in extriangulated categories (2019, background): “[6] A. Beligiannis, The homological theory of contravariantly finite subcategories: Auslander-Buchweitz contexts, Gorenstein categories and (co-)stablization, Comm. Algebra 28 (2000) 4547-4596.”
On singular equivalences of Morita type (2013, unknown): “Indeed, for the simple A-module S one gets Ω(S) S ⊕ S and this implies isomorphisms H(S) HΩ(S)[1] H(S)[1] ⊕ H(S)[1] H(S)[2]4 · · · H(S)[n]2 in Dsg(A).”
Cotorsion pairs, model category structures, and representation theory (2002, methodology): “Other approaches to generalizing the stable module category can be found in [ Bel00 ] and [Jor01].”
On the Freyd categories of an additive category (2000, background): “Note that by [ 11 ], if X is in addition covariantly flnite and any left Xiapproximation has a cokernel in C, then the loop functor ›X admits a left adjoint, the suspension functor §X. In particular if (C;X) is a homotopy pair, then (§X;›X) is an adjoint pair in C=X.”
Cohen-Macaulay modules, (co)torsion pairs and virtually Gorenstein algebras (2005, methodology): “Stabilizations Recall from [18] that to a given left triangulated category C, there is associated in universal way a triangulated category T (C) which reflects many important homologic properties ofC.”