… is called a cotorsion pair (or a cotorsion theory) provided that … these two complete cotorsion
pairs in the category Ch(Flat(X)… (X)) of F-totally acyclic complexes of very flat quasi-coherent …

… In their work, they established their theory in the context of … the C-Gorenstein flat dimension
for complexes. We give … complete hereditary cotorsion pair is the flat cotorsion pair (F, C)…

… are detected by the E2-term of the spectral sequence associated to the filtration of the
total complex by the horizontal degree. We then extend this result to twisted complexes. …

… The study of relative cohomology theory of complexes have … flat (resp., Gorenstein flat)
modules by PGF (resp., GF ). … GP ⊥ ) forms a complete cotorsion pair in C ( R ) . Note that the …

… Recall that a pair (X, Y) of subcategories of A is called a cotorsion pair or cotorsion theory …
In view of Lemma 2.3, we conclude that every complex admits flat-cotorsion resolutions. …

… of the heart and, imitating the arguments on the theory of derivators used by Štovıcek [Što14], …
complexes and N the class of acyclic complexes, the pair (KP, N) is a complete cotorsion …

… dimension, the relative homological theory based on the class of … flat module is a syzygy of
an acyclic complex of flat modules … The cotorsion pair is complete if for any object A ∈ A there …

… ] on the homotopy category of flat modules. Our proof is based … cotorsion pair on the category
C(FPI(A)) we obtained in 3.4, corresponds (via the aforementioned Hovey–Gillespie theory) …

… that starting from a completely hereditary cotorsion pair (A, B) … Flat is the class of flat modules
and follows by Neeman’s [36]. … We will give an overview of the theory of cotorsion pairs and …

… Such a complex is called a totally acyclic complex of injective modules. The syzygies of
this complex are called … With this notation cotorsion theories are just 1-cotorsion theories. …