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.
The symmetric and braided coherence theorems compare S_n with B_n
Remark
Symmetric coherence says that canonical symmetric composites are governed by permutations, hence by . The braided analogue Braided coherence is controlled by underlying braids replaces those permutations by braids, hence by . The quotient map of The braid group surjects onto the symmetric group is exactly the formal operation of imposing , which is why the symmetric theorem is stronger: forgetting the pure-braid kernel is what turns many distinct braided composites into one permutation class.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
13 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
- Saunders Mac Lane, Natural Associativity and Commutativity, Section 4 (standard reference, not scraped)
- Michael Muger, Tensor Categories: A Selective Guided Tour, Sections 2 and 4 (standard reference, not scraped)