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.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Triangulated-category axiom TR3
Definition
TR3 says that if two distinguished triangles have first arrows and , then some makes a morphism of triangles. It is an existence assertion: neither nor the completion is asserted unique.
Depends on
Used by
- Nonuniqueness of a TR3 completion Counterexample
- Triangulated category Definition
- Cones form a functor in every triangulated category False statement
- The third map in a morphism of triangles is unique False statement
- Cone triangles satisfy TR3 Lemma
- The cone object of a map is unique up to nonunique isomorphism 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)