… We prove first (Proposition 3) that, over any ring R, every acyclic complex of projective
modules is totally acyclic if and only if the cycles of every acyclic complex of Gorenstein projective …

… motivation for studying totally acyclic complexes of sheaves … If we define morphisms between
F-totally acyclic complexes … (FlatX) of F-totally acyclic complexes in the homotopy category K…

… a Prj (A)-totally acyclic complex is called a totally acyclic complex of projective objects . In the
… an Inj (A)-totally acyclic complex is called a totally acyclic complex of injective objects; see …

… the homotopy category of totally acyclic R-complexes and that of Q-complexes. This
adjoint pair is … notion of approximations of totally acyclic R-complexes by totally acyclic Q-complexes. …

… question: when is every exact complex of injective modules a totally acyclic one? It is known,
… that every exact complex of injective modules (over arbitrary rings) is totally acyclic. We also …

… that R is Gorenstein if and only if every acyclic complex of projectives is totally acyclic, if and
only if every acyclic complex of injectives is totally acyclic. Theorem II draws attention to the …

… pure acyclic complexes of modules. We obtain several characterizations of these complexes…
of the pure acyclic complexes of flat modules in terms of the complexes of projective …

… Specifically, we provide a classification scheme of totally acyclic complexes by grouping
them based on their decomposition into indecomposable components. That is, we count the …

… complexes and in Gorenstein homological algebra. For example we show that every acyclic
complex … Gorenstein injective) if there exists a totally acyclic complex of projective modules (…

… We prove that the following are equivalent over any ring R: every exact complex of
injective modules is totally acyclic; every exact complex of Gorenstein injective modules is in …