… usual purity theory to this setting, yielding a λ-purity theory. And … complex Y ∈ C(Uco)(X))
dg-cotorsion if each Yn is cotorsion … (Flat(X)) is the class of complexes Y with each Yn cotorsion …

… )-acyclic if the complex of abelian groups HomC(X•, Y) = (HomC(Xm, Y))m∈Z is exact for every
Y ∈ Y. HomC(Y, −)-acyclic complexes … theory of (relative) cotorsion pairs appearing in [3]. …

… A complex I of injective objects is called totally acyclic if it is acyclic and HomA(E, I) is acyclic
… one has G ∼= Z0(I) for some totally acyclic complex I of injective objects in A. In what follows…

… V^\bullet$ is a bounded complex whose terms are all finitely generated Gorenstein
projective … complexes whose terms are finitely generated Gorenstein projective $\Lambda$-modules. …

… Coming from a cotorsion pair, we call it a C-tilting module. For … Recall that a complex (2)
is said to be acyclic if it is … The complexes which are isomorphic to an acyclic complex form a …

… complexes has important applications in theoretical physics, quantum theory and representation
theory … In 2011, Enochs studied Cartan-Eilenberg projective, injective and flat complexes…

… the flat cotorsion theory in the category of modules over an associative ring and the very flat
cotorsion theory … others, play an important role in the theory of contraherent cosheaves [20]. …

… but useful result concerning cotorsion pairs and direct limits (… the class of all acyclic
complexes of geometric pure injective (\(\… the case of K-flat and pure acyclic complexes. Again, \((\…

… X on X is an acyclic complex! 0.9. Let us have a more detailed … [49], we consider a flat affine
morphism of ind-schemes π: Y −→ X. … We discuss the basics of the theory of (strict ind-quasi-…

… In this monograph we develop various aspects of the homotopy theory of exact categories. …
on categories of chain complexes ChpEq which are induced by cotorsion pairs on E. As a …