Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 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.
Exact functor between abelian categories
Definition
Let and be abelian categories. A functor is exact when it is additive (Additive functor) and both left exact and right exact (Left exact and right exact functors).
Thus exactness is a two-sided preservation condition: preserves the finite limits and finite colimits that exist in its source, and it preserves the additive structure carried by the hom-sets.