DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-08-31

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 homotopy category of chain complexes

Definition

Let $A$ be an additive category. The homotopy category of chain complexes on $A$ is the category $K (A) .$ Its objects are the chain complexes in $A$ , and for chain complexes $C_{∙}, D_{∙}$ its morphisms are the homotopy classes ${Hom}_{K (A)} (C, D) : = [C, D]_{K} .$

Composition is induced from composition of representatives and is well defined by Composition of homotopy classes is well defined.

The homotopy category of chain complexes

Definition

Depends on

Dependency tree · 2 levels

Sources