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.
Triangulated-category axiom TR2
Definition
TR2 says that a triangle is distinguished if and only if its signed left rotation is distinguished. In particular, the final arrow of that rotation is the fixed in Rotation of a triangle.
Depends on
Used by
- Triangulated category Definition
- Cone triangles satisfy TR2 with the declared rotation sign Lemma
- Distinguished triangles are closed under shifts and both rotations Proposition
- Zero and split triangles are distinguished Proposition
- Representable Hom functors on a triangulated category are homological or cohomological Theorem
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
- The Stacks Project, Definition 13.3.2 (standard reference, not scraped)