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.
FALSE: a Cat-enriched category is the same thing as a strict 2-category without smallness hypotheses
Statement
A Cat-enriched category is the same thing as a strict 2-category, with no extra size hypotheses.
Facts & Assumptions
Given: The dictionary theorem on the A page.
A Cat-enriched category is exactly a strict 2-category only when the object set is a set and the hom-categories are small (A Cat-enriched category is exactly a strict 2-category with a set of objects and small hom-categories).
Refutation
The theorem [L1] states the precise equivalence and includes the smallness hypotheses as part of the claim.
Removing those hypotheses enlarges the statement beyond [L1], so the displayed unrestricted claim is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
4 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
- Emily Riehl, Categorical Homotopy Theory, Section 3.1 (standard reference, not scraped)