… the existence of a hereditary small cotorsion theory generated by the class of objects of
type \… In this section we study the cotorsion pair cogenerated by all the objects of type \(\textrm{FP}…

… cotorsion theory and FIn is special preenveloping. Moreover if R is left n-coherent, then it is
also shown that the cotorsion theory (… i ), FP⊥ i )=(⊥FIi, FIi) cogenerated by the classes FPi (i …

… F is the torsionfree class and its objects are the torsionfree … envelopes, then the tilting class
is cogenerating, meaning that for … Another particular case of torsion theories in a Grothendieck …

… torsionfree class is closed under direct limits and describe them in terms of approximation
theory and cosilting theory… (3) For the torsion pair cogenerated by CS we have again that every …

… play in torsion theory. If (T , F) is a torsion pair in Mod-R, then the torsion free class F always
… If T is a pure projective 1-tilting module, then, because the tilting class Gen T is cogenerating…

… for a large class of groups: the cotorsion groups (ie groups whose extensions by torsion-free …
and from [5, (54.5)] that a torsion-free group is cotorsion iff it is algebraically compact (ie G is …

… In this section, we recall the basics of approximation theory for … the Enochs cotorsion pair
is cogenerated by the class of all … Note that Mod–Q (= the class of all divisible torsion-free R-…

… problem from the viewpoint of tilting theory. Using the methods … C[1]={}^\perp C[1]\) is a
torsionfree class in \(\mathcal {A}\). Let \(X\… torsion-free, if it is torsion, respectively torsion-free, with …

… a hereditary small cotorsion theory generated by the class of … cogenerated by a set in any
locally type FPn category. §5 is … , MA, Torsion and torsion-free classes from objects of finite type …

… Using the notion of a cotorsion pair, we study generalizations … of all torsion free modules is
a cofactorization class of gn h . … Then C is a cotilting cotorsion pair, ie, C is cogenerated by a …