… 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 …

… finish this chapter by proving that any complex is qùasi-isomorphic to a minimal DG-injective
one. This result gives another interpretation of the derived category … category A is a pair (T, T…

… 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 …

… N-complexes. In Section 3, we start with a cotorsion pair (X , Y ) in an abelian category A …
We prove that if the cotorsion pair (X , Y ) is complete and hereditary in a bicomplete abelian …

… We consider a complete hereditary cotorsion pair ( A , B ) … category, we consider triples of
examples of injective and projective cotorsion pairs on the categories of unbounded complexes …

… of complete cotorsion pairs… complexes (see Theorem 5.41). We also prove in Theorem
5.39 that if A is part of a certain left n-cotorsion pair of complexes, then ( A , B ) is a left n-cotorsion …

… N-complexes. In Section 3, we start with a cotorsion pair (X , Y ) in an abelian category A …
We prove that if the cotorsion pair (X , Y ) is complete and hereditary in a bicomplete abelian …

… a complete hereditary cotorsion pair in general. Let (A, L) be a complete hereditary cotorsion
pair … Then, by [12, 25], (dg A, L) is a complete hereditary cotorsion pair in the category of R-…

… of chain complexes over C ; see for … (co)complete category without depending on generation
arguments, and extends the class of cotorsion pairs for which the induced cotorsion pairs (ii'…