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.
Enriched naturality can be strictly stronger than ordinary naturality of the underlying components
Remark
The data of a -natural transformation are only the components (Enriched natural transformation), so at first sight they look like the components of an ordinary natural transformation between the underlying functors. The content sits in the naturality equation: The lozenge and compact-square forms of enriched naturality are equivalent requires a commuting square in the base category , not merely a commuting square after applying the underlying-set or underlying-hom functor. For bases such as or differential graded modules, that enriched square retains morphism-level information that the underlying ordinary naturality equation forgets.
Depends on
Used by
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, Remark 3.5.11 (standard reference, not scraped)