DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-30

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.

The category of chain complexes

Definition

The category of chain complexes in an abelian category $A$ is denoted $Ch (A) .$ Its objects are chain complexes in $A$ , and its morphisms are chain maps.

By Identities and composites of chain maps are chain maps, identities and composition are defined degreewise.

The full subcategories on bounded below, bounded above, and bounded complexes are denoted ${Ch}^{+} (A), {Ch}^{-} (A), {Ch}^{b} (A) .$

The category of chain complexes

Definition

Depends on

Dependency tree · 2 levels

Sources