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 library does not use Freyd-Mitchell to prove the diagram lemmas
Freyd-Mitchell is not the proof device for this library's later diagram lemmas. It applies only to small abelian categories, it is not proved in this batch, and it would make the later exactness pages depend on a metatheorem rather than on the intrinsic abelian arguments built from pullbacks, pushouts, images, and cokernels.
That trade is the wrong one for the library. The member calculus and the diagram-lemma pages stay internal to an arbitrary abelian category, with no smallness side condition and no appeal to an ambient module category.
Depends on
Used by
Nothing in the library uses this result yet.
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
- Peter Freyd, Abelian Categories, Chapter 7 (standard reference, not scraped)
- Junhan Tan, The Freyd-Mitchell Embedding Theorem (standard reference, not scraped)