… and their relations to approximation theory of infinitely generated modules over arbitrary …
tilting and cotilting modules, and characterize the induced tilting and cotilting cotorsion pairs. §4 …

… Given a ring R and a cotorsion pair C = (A, B), we consider closure … cotorsion pairs for
dualizing to cotilting modules some of the recent results on (infinitely generated) tilting modules. …

… finiteness properties of cotilting torsion and cotorsion pairs. Any cotilting module is pure-…
, we will focus on torsion and cotorsion pairs induced by Σ -pure-injective cotilting modules. …

… that U is cotilting if the cotorsion-free class of the cotorsion theory generated … cotorsion
theory generated by a class of pure-injective modules is complete and, as noted above, a cotilting …

… In the finite dimensional case, Auslander and Reiten studied approximations of modules
induced by tilting and cotilting modules [7]. This theory has recently been extended to arbitrary …

… ABSTRACT We study a duality between (infinitely generated) cotilting and tilting modules …
show that a module P is partial cotilting iff P is a direct summand of a cotilting module C such …

… With a view to following this approach, we show in Theorem 1.13 that equivalence classes
of cotilting modules over left artinian rings are parametrised by maximal sets of pairwise Ext-…

… ⊥ T for any cotilting module T, since T = Λ is the only cotilting module over Λ up to
additive closure. Considering C ⊥ gives an example of an extension for statement (2). …

… In addition, we discuss the n-cotilting and n-tilting cotorsion pairs, for which we obtain
better … cotorsion pairs related to the contraderived and coderived categories of curved DG-modules…

… cotilting theory of (arbitrary) modules which are summarized in the following. A module C ∈
MR is a cotilting module … an Enochs cotorsion module, cf. [10]. In fact more is true: by [4], any …