… of whether or not the induced cotorsion pairs are complete when the original cotorsion pair
is complete, and shown that a cotorsion pair (A, B) in an abelian category C can induce two …

… The definition of cotorsion pair appears as Definition 2.2 and Hovey’s … an abelian category
with enough injectives. We will call a complete cotorsion pair (W, F) an injective cotorsion pair …

… We introduce a notion of total acyclicity associated to a subcategory of an abelian … -totally
acyclic complexes. In the context of a cotorsion pair (U , V), we show that the categories of right …

… The definition of cotorsion pair appears as Definition 2.2 and Hovey's … abelian category
with enough injectives. We will call a complete cotorsion pair ( W , F ) an injective cotorsion pair …

… We show that if the given cotorsion pair (A, B) in the category of modules is complete and
hereditary, then both of the induced cotorsion pairs in the category of complexes are complete. …

… of exact complexes, DG-injective and DG-projective complexes. We finish this chapter by …
We recall that a torsion theory for an abelian category A is a pair (T, T) of classes of objects …

… category and (𝒳,𝒴) a complete and hereditary cotorsion pair … of 𝒳 complexes by 𝒳 ̃ and the
class of dg𝒳 complexes by d g … complexes is denoted by 𝒴 ̃ and the class of dg𝒴 complexes …

… cotorsion pair (C∩W,F) consists of the exact complexes and the DG-injective complexes. …
We will prove that (C,F∩W) is a functorially complete cotorsion pair with respect to P. The proof …

… a cotorsion pair on an abelian category to a model structure on chain complexes over that
category… enough injectives, we say that it is a complete cotorsion pair. Perhaps the most useful …

… general abelian categories and have proved useful in a variety of settings. In this article we
will consider complete cotorsion pairs (C, V) in the category C(R-Mod) of complexes of left R- …