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.

Cochain map

Definition

Let $C^{∙}$ and $D^{∙}$ be cochain complexes. A cochain map $f : C^{∙} \to D^{∙}$ is a family of morphisms $f^{n} : C^{n} \to D^{n}$ such that $d_{D}^{n} \circ f^{n} = f^{n + 1} \circ d_{C}^{n}$ for every $n \in Z$ .

Thus the upper-index square $\begin{array}{ccc} C^{n} & \overset{f^{n}}{\to} & D^{n} \\ d_{C}^{n} ↓ & ↓ d_{D}^{n} \\ C^{n + 1} & \overset{f^{n + 1}}{\to} & D^{n + 1} \end{array}$ commutes in each degree.

Depends on

Cochain complex in an abelian category

Cochain map

Definition

Depends on

Dependency tree · 2 levels

Sources