DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-01

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.

Injective resolutions in an abelian category

Definition

Let $A$ be an object of an abelian category. An injective resolution of $A$ is a coaugmented cochain complex $0 \to A \overset{η}{\to} I^{0} \to I^{1} \to I^{2} \to \dots$ such that every $I^{n}$ is injective and the coaugmented complex is exact at every displayed term.

Thus the object $A$ sits as the initial term of an exact cochain complex of injective objects.

Injective resolutions in an abelian category

Definition

Depends on

Dependency tree · 2 levels

Sources