DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-11

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.

Diagram as a functor from an indexing category

Definition

A diagram in a category $C$ is a functor $D : J \to C$ (Covariant functor, identity functor, composite functor, and contravariant functor) from an indexing category $J$ . The shape of the diagram is $J$ . Thus objects and arrows of $J$ name objects and commuting composites displayed in $C$ . All relations in $J$ are preserved by functoriality.

Depends on

Covariant functor, identity functor, composite functor, and contravariant functor

Dependency tree · 2 levels

Sources

Emily Riehl, Category Theory in Context, Chapter 1