… 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 …

… 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-…

… 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 …

… 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, ( …

… of this theory of Beligiannis in persistence theory and … τcotorsion torsion triples with the
left weak cotorsion torsion … To show that it is a torsion free class, we need to show that it …

… a natural cotorsion theory related to these two classes when there … , if the pair (F;F?) is
cogenerated by a set then evry object M 2 Ob(A… of the class of arbitrary R-torsionfree RG-modules. …

… This chapter will explore the properties of cotorsion theories and demonstrate how to construct
a homology theory for any cotorsion pair. In this chapter, the class of modules discussed …

… to establish our results: the theory of purity in locally finitely … X) we denote the class of all
objects Y cogenerated by X, that … classes in H coincide with the generating torsion-free classes, …

… Recall that an R-module is finitely cogenerated if its injective … a well-defined structure theory
for a class of modules, then we … C is cotorsion if every extension of C by a torsion-free group …