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: the underlying ordinary category determines the enriched category
Statement
The underlying ordinary category determines the full enriched category.
Facts & Assumptions
Given: The information-loss remark from the A page.
The underlying category can lose enriched information, for instance 2-cells in Cat-enrichment (The underlying category can lose genuinely enriched information).
Refutation
By [L1], distinct enriched hom-objects can induce the same underlying ordinary hom-set data.
Therefore the underlying ordinary category does not determine all enriched structure, so the statement is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
2 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 3.4 (standard reference, not scraped)