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.
A quasi-isomorphism has an acyclic cone in the triangulated language
Statement
If is a quasi-isomorphism, its standard cone triangle has an acyclic third object.
Facts & Assumptions
Given: A quasi-isomorphism of complexes in an abelian category.
Proof
The standard cone triangle has third object .
A chain map is a quasi-isomorphism exactly when its cone is acyclic, so this third object is acyclic.
Depends on
Used by
Dependency tree · two levels
12 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 13.9.1 (standard reference, not scraped)