Tilting Preenvelopes and Cotilting Precovers

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Covers, precovers, and purity (2008, background): “3; the book [10] is a useful reference, but see also [2], [3], [7], [11], and [13].”
Silting modules (2014, background): “They play an important role in approximation theory, since they correspond bijectively to the tor sion classes that provide special preenvelopes (see [9]).”
Cotilting modules over tame hereditary algebras (2003, result): “In [2], a similar result is proved under the additional hypothesis that X is contravariantly finite.”
A characterization of n-cotilting and n-tilting modules (2004, result): “As proved in [2,6,7], the above definitions are respectively equivalent to the follow Definition 2.”
COVERS, ENVELOPES, AND COTORSION THEORIES (2000, methodology): “This theory has recently been extended to arbitrary modules [4], [ 5 ], [19].”
Tilting theory and the finitistic dimension conjectures (2002, background): “Again, it is a common generalization of the classical finite-dimensional case [5] and the case of infinitely generated modules of projective dimension at most one [3].”
Tilting Modules Arising from Ring Epimorphisms (2008, methodology): “We start with an extension of [ AHHT05 , Proposition 6.4].”