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 strong enriched Yoneda lemma for a large category constructs the whole enriched functor category
Statement
For a large enriched category, the strong enriched Yoneda lemma automatically constructs the whole enriched functor category.
Facts & Assumptions
Given: The strong Yoneda theorem and its size warning.
The strong enriched Yoneda lemma constructs a particular end (Strong enriched Yoneda lemma as a particular end).
That particular end is a different size claim from the existence of the whole enriched functor category (The particular Yoneda end and the enriched functor category have different size requirements).
Full faithfulness of the Yoneda assignment does not add the missing large-source functor-category existence hypothesis (The enriched Yoneda assignment is fully faithful).
Refutation
The theorem [L1] proves only the existence of one end attached to one representable functor.
By [L2], that does not construct the whole enriched functor category for a large source, and [L3] does not change that size issue. Therefore the statement is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
9 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, Sections 2.2 and 2.4 (standard reference, not scraped)