DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-04

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Sheafification of a presheaf

Definition

Let $F$ be a presheaf on a topological space $X$ .

Its sheafification is the sheaf $a F : = F^{+ +} .$

The canonical morphism $η_{F} : F ⟶ a F$ is the composite $F \overset{η}{\to} F^{+} \overset{η}{\to} (F^{+})^{+} = a F,$ where each $η$ is the single-chart map of The plus construction for a presheaf.

By The second plus construction is a sheaf, $a F$ is indeed a sheaf.

Sheafification of a presheaf

Definition

Depends on

Dependency tree · 2 levels

Sources