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.