THM0120canonicalv1H⁰ = Global Sections
H⁰ equals the space of global sections. For the constant sheaf, a 0-cochain is a global section iff it is constant. Non-constant functions have nonzero coboundary.
Payload
H⁰ = Global Sections
H⁰ equals the space of global sections. For the constant sheaf, a 0-cochain is a global section iff it is constant. Non-constant functions have nonzero coboundary.
H⁰ = Global Sections
Summary
H⁰ equals the space of global sections. For the constant sheaf, a 0-cochain is a global section iff it is constant. Non-constant functions have nonzero coboundary.
Statement
No manuscript statement was extracted in this pilot run.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-02.jsonlline 214 - Manuscript source: not matched
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookII.CentralTheorem.SheafCohomology - Name:
h0_global_2
Dependencies
- Canonical: II.D87
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
II.T55h-global-sectionsthm:h0-globalRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (3)
Appears in (1)
Downstream uses (computed) (6)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
FTH0163formal theorem
FTH0163formal theorem
FTH0164formal theorem
FTH0164formal theorem
FTH0165formal theorem
FTH0165formal theoremSources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.