DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

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.

Effaceable cohomological delta functor in positive degrees

Definition

Let $T = (T^{n}, \partial)$ be a cohomological delta functor on an abelian category $A$ . We say that $T$ is effaceable in positive degrees by injectives when for every $n > 0$ and every object $A$ of $A$ , there exists a monomorphism $u : A ↣ I$ with $I$ injective such that the induced map $T^{n} (u) : T^{n} (A) \to T^{n} (I)$ is zero.

Again, the definition only asks for existence object by object and degree by degree.

Effaceable cohomological delta functor in positive degrees

Definition

Depends on

Dependency tree · 2 levels

Sources