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.
The direct preservation theorem carries no size hypothesis
The proof of Right adjoints preserve every limit that exists transposes individual cone legs by explicit unit and counit formulas. It neither collects a hom-class into a set nor forms a Set-valued representable functor. Consequently its statement applies to every legitimate diagram whose limit exists, without assuming local smallness of the categories or smallness of the indexing category. The separate representable proof needs both hypotheses because its chain of hom-set isomorphisms is Set-valued.
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, Category Theory in Context, 2nd ed., Section 4.6 (standard reference, not scraped)