… F n as torsion and torsion-free classes, respectively, are given … used in module theory and
representation theory of Artin … In particular, every cotorsion pair cogenerated by a set in a …

… equivalent if they cogenerate the same cosilting class, which … classes are precisely the
definable torsion-free classes, cf. [6, … We consider the tilting cotorsion pair (A, Gen TA) induced by …

… For its applications in approximation theory, relative homological algebra, and tilting theory,
… ) the torsion-free quotient of X. A torsion pair t = (T , F) is said to be hereditary if the class T is …

… If these two cotorsion pairs are also cogenerated by sets, … ] and Salce [33], a cotorsion pair
is a pair of classes (X, Y) in D … Gorenstein flat if and only if it is strongly torsionfree. (3) A left R-…

… ; namely, we consider torsion-free classes which are of the form … in Mod-R are exactly the
classes which are cogenerated by … For the general theory of semiperfect rings we refer to [2]. …

… We also show that tilting theory is intimately related to … the torsion-free classes under the
correspondence from Proposition 2.12. This was important in the classification of tilting classes …

… Cotorsion pairs and approximations We start by recalling the fundaments of the theory of
cotorsion … , C is a definable torsion-free class, and thus C is a torsion-free class in a hereditary …

… The following important result about cotorsion pairs generated by sets of modules will be
used … The following observation will be useful in characterizing cotilting torsion-free classes of …

… the right constituents of right complete cotorsion pairs and, when A has an … If there is a
cogenerating class X ⊆ V … TTF class if it is both a torsion and a torsion-free class; in this last case, ( …

… T and H on the generating or cogenerating classes, rK ↦− → rH… mappings and in this case
they preserve torsions or cotorsions. … Every torsion free class (ie of the form Fr for a torsion r) is …