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.
Distinguished triangle
Definition
Given a category with translation, a distinguished triangle is a triangle belonging to a specified class . The requirements on are the four axioms stated next; only after those axioms are imposed may it also be called an exact triangle.
Depends on
Used by
- Triangulated category Definition
- Triangulated-category axiom TR1 Definition
- Triangulated-category axiom TR2 Definition
- Triangulated-category axiom TR3 Definition
- Triangulated-category axiom TR4 (octahedral) Definition
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
- The Stacks Project, Definition 13.3.2 (standard reference, not scraped)