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.

Coaugmented cochain complexes under an object

Definition

Let $A$ be an object of an abelian category. A coaugmented cochain complex under $A$ is a cochain complex in nonnegative degrees $I^{0} \overset{d^{0}}{\to} I^{1} \overset{d^{1}}{\to} I^{2} \overset{d^{2}}{\to} \dots$ together with a morphism $η : A \to I^{0}$ such that $d^{0} η = 0.$

Equivalently, one has an extended cochain $0 \to A \to I^{0} \to I^{1} \to I^{2} \to \dots$ whose consecutive composites are zero.

Depends on

Cochain complex in an abelian category

Coaugmented cochain complexes under an object

Definition

Depends on

Dependency tree · 2 levels

Sources