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.
Rigidity alone does not make a tensor category
Remark
EGNO's term tensor category is much stronger than "rigid monoidal category". Their Definition 4.1.1 requires a locally finite -linear abelian rigid monoidal category over an algebraically closed field with , and Definition 4.2.3 similarly adds the ambient hypotheses for multitensor categories.
So this page may use rigidity, pivotality, sphericality, twists, and ribbon structure, but it may not silently import fusion-category or Grothendieck-ring consequences whose proofs need those extra hypotheses.
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, Definitions 4.1.1 and 4.2.3 (standard reference, not scraped)