theorem · fr-2-theorem-8-10
Fixed-Source Descent Decomposition
Result stated and proved in the source manuscript; website restatement fusion-reconstruction
Statement
Under Assumption 8.1, the set-valued tight reconstruction presheaf satisfies the sheaf condition on a cover exactly when every matching family has an admissible amalgam and the cover has recognition.
Meaning and scope
Amalgamation supplies existence; recognition supplies uniqueness up to the chosen equivalence. This is a fixed-source, set-valued theorem.
The paper page includes the reader corrections accompanying this edition.
Source
Paper 2, Theorem 8.10. Research note — not peer reviewed.
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