Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-28
How 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.
Abelian category
Definition
An abelian category is an additive category (Additive category) in which every morphism has a kernel and a cokernel, and in which for every morphism the canonical comparison morphism
constructed in The canonical morphism from the coimage to the image exists and is unique is an isomorphism.
The first two clauses are Grothendieck's AB1, while the invertibility of the canonical map is this page's working form of AB2.