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.
FALSE: the connecting morphism depends on the choices made in its construction
Statement
The connecting morphism in the snake lemma depends on the choices made during its construction.
Facts & Assumptions
Given: The arrow-theoretic construction of the connecting morphism.
The connecting morphism exists and is unique (The connecting morphism exists and is unique).
Consequently, no choice-independence argument remains to be proved (The connecting morphism depends on no choices).
Refutation
The statement of [L1] already says that the connecting morphism is the unique map making one displayed square commute.
By [L2], uniqueness is exactly what rules out any dependence on auxiliary choices. Therefore the statement is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
10 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)