… 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-…

… 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 …

… modules, silting classes, torsion theories and linear topologies. … for cotorsion pairs cogenerated
by a particular class which we … a 1cotilting cotorsion pair and the torsion-free class ⊥C is …

… 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. …

… it is obtained from a torsion pair cogenerated by a cotilting object. At … Afterwards, we outline
the theory of torsion pairs in a … Finally, we know that CogenW is a torsionfree class in G in the …