DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + claude-opus-5[1m])audited 2026-08-24

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.

Reflexive parallel pairs and reflexive coequalizers

Definition

A parallel pair $f, g : A ⇉ B$ is reflexive when it has a common section: there is a morphism $r : B \to A$ such that

$f r = g r = 1_{B} .$

A reflexive coequalizer is a coequalizer (Equalizers and coequalizers as limits and colimits of a parallel pair) of a reflexive parallel pair.

Depends on

Equalizers and coequalizers as limits and colimits of a parallel pair

Used by

A reflexive coequalizer of sets not preserved by Set(ℕ,-) Counterexample
Data-supplied crude monadicity theorem for reflexive coequalizers Theorem

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

E. Riehl, Category Theory in Context, 2nd ed., Proposition 5.5.8 (standard reference, not scraped)