DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)audited 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 $\mathcal C$ is a functor $D:\mathcal J\to\mathcal C$ (Covariant functor, identity functor, composite functor, and contravariant functor) from an indexing category $\mathcal J$ . The shape of the diagram is $\mathcal J$ . Thus objects and arrows of $\mathcal J$ name objects and commuting composites displayed in $\mathcal C$ . All relations in $\mathcal J$ are preserved by functoriality.

Depends on

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

Used by

Nothing in the library uses this result yet.

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 5 results over 4 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

Emily Riehl, Category Theory in Context, Chapter 1 (standard reference, not scraped)