… 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 …

… 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…

… And we also characterize the left orthogonal class of exact complexes of injective modules
and the classes of modules with finite Gorenstein projective, Gorenstein flat, and PGF …

… 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-…

… complete hereditary cotorsion pairs in abelian categories A and B can induce complete
hereditary cotorsion pairs … Let A be an abelian category and X a complex in A. With homological …

… 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 …

… , in particular for the category of N-complexes. In this work, … complete cotorsion pairs in the
category of N-complexes. One method to create such pairs is to start with two cotorsion pairs …

… and certain complete cotorsion pairs (F, … complete cut cotorsion pairs, cut Frobenius pairs,
and cut weak AB contexts related to relative Gorenstein homological algebra, chain complexes…

… there is a bijection between complete cotorsion pairs in C and … between complete cotorsion
pairs and cotorsion pairs in [14… a cotorsion pair in [24] will be called a complete cotorsion pair …

… nice cotorsion pairs, then we find model structures on their categories of chain complexes. …
By assumption the cotorsion pairs (Di,Ei) are complete and we find E ∈ E0 together with a …