DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge 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.

A morphism of short exact sequences of complexes

Definition

A morphism of short exact sequences of complexes is a commutative ladder $\begin{array}{ccccccccc} 0 & \to & A_{∙} & \to & B_{∙} & \to & C_{∙} & \to & 0 \\ ↓ & ↓ & ↓ \\ 0 & \to & A_{∙}^{'} & \to & B_{∙}^{'} & \to & C_{∙}^{'} & \to & 0 \end{array}$ in which each row is a short exact sequence of complexes and each vertical map is a chain map.

Equivalently, it is a triple of chain maps $a : A_{∙} \to A_{∙}^{'}$ , $b : B_{∙} \to B_{∙}^{'}$ , and $c : C_{∙} \to C_{∙}^{'}$ for which the obvious squares with the inclusion and projection maps commute in every degree.

A morphism of short exact sequences of complexes

Definition

Depends on

Dependency tree · 2 levels

Sources