DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17

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.

Conservative functor

Definition

A functor $U : D \to C$ is conservative if it reflects isomorphisms: whenever $f$ is a morphism of $D$ and $U (f)$ is an isomorphism in $C$ (Isomorphism, groupoid, and connected category), the morphism $f$ is an isomorphism in $D$ .

Depends on

Used by

Every monadic functor is conservative Theorem

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 6 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

E. Riehl, Category Theory in Context, 2nd ed., discussion following Lemma 5.6.1 (standard reference, not scraped)