Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedprecheck passaudited 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.

FALSE: every braided monoidal category is equivalent to a strict commutative one

Statement

False claim: every braided monoidal category is braided-monoidally equivalent to a strict braided monoidal category whose braiding is the identity on every tensor product.

Facts & Assumptions

Given: The braid category and strict braided strictification.

[L1]

The braid category is braided but not symmetric (The braid category is braided but not symmetric).

[L2]

Every braided monoidal category is braided-monoidally equivalent to some strict braided monoidal category (Every braided monoidal category is monoidally equivalent to a strict braided one).

Refutation

technique · direct
1.1

Apply the claim to the braid category from [L1]. Then there would exist a braided monoidal equivalence from B to a strict braided category D whose braiding is the identity.

L1givenassume-contra
2.1

A strict braided category with identity braiding is symmetric, because its braiding certainly squares to the identity. Transporting that symmetric structure back across the supposed braided equivalence would make B symmetric as well.

L2step 1.1algebra
3.1

Step 2.1 contradicts [L1], which says the braid category is not symmetric. Therefore the claim is false.

L1step 2.1discharge-contradiction∎

Depends on

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