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: every enriched category has constant enriched functors
Statement
Every enriched category admits constant enriched functors.
Facts & Assumptions
Given: The A-page obstruction theorem.
Constant enriched functors need not exist (Constant enriched functors need not exist).
Refutation
The theorem [L1] gives an enriched category whose underlying ordinary constant functor has no enriched lift.
That witness contradicts the universal assertion in the statement. Hence the statement 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
- G. M. Kelly, Basic Concepts of Enriched Category Theory, Section 3.9 (standard reference, not scraped)