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.
Snake data
Definition
A piece of snake data in an abelian category means one of the following commutative diagrams.
The Mac Lane shape is a morphism of short exact sequences
The weaker Stacks shape is a commutative diagram
whose top and bottom rows are exact.
This page uses the name only for the data of the diagram and its exact rows. The connecting morphism and the snake sequence attached to such data are constructed later.
Depends on
Used by
Dependency tree · two levels
2 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
- Saunders Mac Lane, Categories for the Working Mathematician, Lemma VIII.4.5 (standard reference, not scraped)
- The Stacks Project, Section 12.5, Lemma 12.5.17 (standard reference, not scraped)