Alphabeta Math
RemarkRemark: Literature-sourcedProof: Not applicableaudited 2026-08-31
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.

The historical route to coherence and the route authored here

Remark

Mac Lane's 1963 paper proved coherence by a direct rank-induction analysis of formal associativity and unit laws, and How Mac Lane's original coherence conditions reduce to this page's two axioms records the older five-condition formulation from that period. The theorem itself is therefore historically Mac Lane's.

The route authored on this page is different. Following EGNO's attribution, the proof of Mac Lane strictification is the later Joyal-Street strictification argument, and Mac Lane coherence in canonical-map form is obtained from it by transporting canonical maps to a strict monoidal target. So the page keeps the historical origin visible while deliberately choosing the strictification route as the local proof.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

15 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