Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-01
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.
Braided monoidal category
Definition
A braided monoidal category is a monoidal category together with a chosen braiding in the sense of Braiding.
Depends on
Used by
- Braided monoidal functor Definition
- Symmetric monoidal category Definition
- The braid category Definition
- In a strict braided monoidal category the braiding satisfies the Yang-Baxter equation Theorem
- Monoid objects in a braided monoidal category form a monoidal category Theorem
- The double-braiding center is a symmetric monoidal subcategory Theorem
Dependency tree · two levels
3 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, Chapter 8.1 (standard reference, not scraped)