On the abstract Čech cohomology

The present Note is a survey of the authors' papers [11, 12, 14, 16–18], concerning the introduction and study of the notion of the abstract Čech cohomology, as well as its applications. Here we have investigated: projective systems, injective systems, covering of a directed partially ordered set, abstract Čech cohomology, abstract Čech homology, Čech cohomology space, simplicial projective systems, de Rham cohomology space of projective systems, J-resolution of a projective system and acyclic resolution.