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: an enriched natural transformation is only a natural transformation of the underlying functors
Statement
An enriched natural transformation is nothing more than an ordinary natural transformation between the underlying functors.
Facts & Assumptions
Given: The strengthened-naturality remark from the A page.
Enriched naturality is strictly stronger than ordinary naturality of the underlying components (Enriched naturality can be strictly stronger than ordinary naturality of the underlying components).
Refutation
The theorem-page remark [L1] already identifies the failure: the component data may look ordinary, but the enriched naturality square asks for more.
So the statement that enriched naturality is only ordinary naturality 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
- Emily Riehl, Categorical Homotopy Theory, Section 3.5 (standard reference, not scraped)