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.
Strictification requires the axiom of choice
Statement
False claim: Mac Lane strictification requires the axiom of choice.
Facts & Assumptions
Given: The choice-cost boundary for strictification.
The strictification theorem itself is a functorial construction and does not use choice; only the stronger skeletal refinement has that cost (Strictification itself costs no Choice; choosing a skeleton can).
Refutation
If strictification itself required choice, then the theorem's own construction would already depend on selecting representatives.
But [L1] states that the selection occurs only in the stronger skeletal refinement, not in strictification itself.
Therefore the claim is false.
Depends on
Used by
Nothing in the library uses this result yet.
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, Exercise 2.8.8 (standard reference, not scraped)