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: in an abelian category a morphism can be monic and epic without being an isomorphism
Statement
In an abelian category, a morphism can be monic and epic without being an isomorphism.
Facts & Assumptions
Given: An abelian category.
Abelian categories are balanced (An abelian category is balanced).
Refutation
The statement asserts the existence of a bimorphism in an abelian category that is not an isomorphism.
But [L1] says every bimorphism in an abelian category is an isomorphism. So the asserted witness cannot exist, and the statement is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
5 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
- Junhan Tan, The Freyd-Mitchell Embedding Theorem, Theorem 2.4 (standard reference, not scraped)