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On the abstract Čech cohomology. (English) Zbl 1306.55002
Summary: The present Note is a survey of several papers by the authors, 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.
MSC:
55N05 Čech types
55T25 Generalized cohomology and spectral sequences in algebraic topology
55N35 Other homology theories in algebraic topology
55N30 Sheaf cohomology in algebraic topology
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
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