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.
Coherence says that any two parallel morphisms in a monoidal category are equal
Statement
False claim: coherence says that any two parallel morphisms in a monoidal category are equal.
Facts & Assumptions
Given: The scope remark for the coherence theorem.
Coherence compares only canonical morphisms between parenthesisations of one ordered tensor word; arbitrary parallel morphisms lie outside its scope (The coherence theorem's exact scope).
Refutation
If the claim were true, the theorem would identify every parallel pair in the category, with no restriction on how those morphisms were built.
That contradicts [L1], which records the theorem's actual quantifiers and restricts it to canonical structural morphisms.
Therefore the claim is false.
Depends on
Used by
Nothing in the library uses this result yet.
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
- P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories, Theorem 2.9.2 (standard reference, not scraped)