Alphabeta Math
CorollaryStatement: Literature-sourcedProof: AI-adaptedSession-authored (Fable 5 assisted)precheck passaudited 2026-08-13
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.

Every equalizer is a monomorphism, and every coequalizer is an epimorphism

Statement

Every equalizer morphism is monic, and every coequalizer morphism is epic.

Facts & Assumptions

Given: An equalizer e:E→A and a coequalizer q:B→Q.

[F1]

An equalizer is the single nonidentity leg of a limiting cone, and a coequalizer is the single nonidentity leg of a colimiting cocone (Equalizers and coequalizers as limits and colimits of a parallel pair).

[L1]

Limit legs are jointly monic and colimit legs are jointly epic (The legs of a limiting cone are jointly monic, and the legs of a colimiting cocone are jointly epic).

Proof

technique · direct corollary
1.1

If er=es, [F1] and the limiting clause of [L1] give r=s; hence e is monic.

F1L1
2.1

If rq=sq, [F1] and the colimiting clause of [L1] give r=s; hence q is epic.

F1L1∎

Depends on

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: 10 results over 7 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