Alphabeta MathHow 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.
How Mac Lane's original coherence conditions reduce to this page's two axioms
Mac Lane's 1963 Theorem 5.2 lists five coherence conditions involving the associator and unit constraints. The present page starts from only the pentagon and triangle of Monoidal category. The gap is closed by the three later items on this page:
- The left unitor of a tensor product is determined by the associator recovers the left unit formula;
- The right unitor of a tensor product is determined by the associator recovers the right unit formula;
- The two unitors agree on the tensor unit recovers the equality on the unit object.
So the page's two axioms and Mac Lane's larger historical package define the same notion; the extra conditions become theorems rather than axioms.
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Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
7 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
- S. Mac Lane, Natural Associativity and Commutativity, Theorem 5.2 (standard reference, not scraped)
- S. Mac Lane, Categories for the Working Mathematician, Chapter VII.1 (standard reference, not scraped)