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DerivedAlgGeo.CategoryTheory.Sites.SheafCohomology.Cech

Čech complexes on a site #

The Čech nerve and cosimplicial object of a covering family, its cochain complex and bicomplex against an injective resolution, contractibility, the first page, the forgetful comparison to abelian groups, the total-complex comparison with derived sheaf cohomology, and injective resolutions on a small site. Every signature here uses an arbitrary Grothendieck topology. The results that mention a topological space and its opens, including the global-sections comparison, live in Topology/Sheaves/Cech/; Comparison and ComplexNaturality import that half, as Mathlib's Sites/Spaces.lean imports Topology/Sets/Opens.