Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-31
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.

Every monoidal category is monoidally equivalent to a skeletal strict one

Statement

False claim: every monoidal category is monoidally equivalent to a strict monoidal category that is also skeletal.

Facts & Assumptions

Given: The meaning of skeletal category and the scope warning about strictification.

[L1]

A skeletal category is one in which isomorphic objects are equal (Skeletal category and skeleton).

[L2]

The strictification remark records that one cannot in general ask for a model that is both strict and skeletal at once (Strictification gives equivalence, not on-the-nose identification).

Refutation

technique · direct
1.1

By [L1], adding the word "skeletal" strengthens the strictification target by requiring equality of all isomorphic objects there.

L1
1.2

But [L2] states that this stronger simultaneous requirement can fail even though ordinary strictification succeeds.

L2
2.1

Hence the claim is false.

step 1.1step 1.2∎

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