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.
An abelian category has all finite limits and all finite colimits
Statement
Every abelian category has all finite limits and all finite colimits.
Facts & Assumptions
Given: An abelian category .
An abelian category is additive and every morphism has a kernel and a cokernel (Abelian category).
An additive category with all kernels and cokernels has all finite limits and all finite colimits (An additive category with all kernels and cokernels has all finite limits and colimits).
Proof
By [L1], an abelian category satisfies the hypotheses of [L2].
Therefore [L2] applies directly and yields all finite limits and all finite colimits.