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: every additive category with all kernels and cokernels is abelian
Statement
Every additive category with all kernels and cokernels is abelian.
Facts & Assumptions
Given: The filtered-vector-space category from Filtered vector spaces can be additive with kernels and cokernels without being abelian.
The filtered-vector-space example is additive and has all kernels and cokernels, but it is not abelian (Filtered vector spaces can be additive with kernels and cokernels without being abelian).
Refutation
The cited category satisfies the hypothesis of the statement: it is additive and has kernels and cokernels.
But [L1] also says that category is not abelian. Therefore the universal statement is false.
Depends on
Used by
Nothing in the library uses this result yet.
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, Section 12.3, Example 12.3.13 (standard reference, not scraped)