… 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…

… 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 …

… 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'…

… 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 …

… 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 …

… 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 …

… which asserts that a cotorsion pair (A,B) in M induces cotorsion pairs ( A,dg B) and (dg A, B)
in the category Ch(M) of chain complexes in M. … in M which is generated by a set is complete.…