Alphabeta MathTheoremStatement: Literature-sourcedProof: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-29
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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.
Epimorphisms in an abelian category are universal
Statement
Every epimorphism in an abelian category is universal: every pullback of it is again an epimorphism.
Facts & Assumptions
Given: An epimorphism in an abelian category and any pullback of it.
[L1]
The pullback of an epimorphism is an epimorphism (The pullback of an epimorphism is an epimorphism).
Proof
technique · direct
1.1given
Take any epimorphism and any pullback of it.
2.1L1step 1.1∎
The pullback leg is epic by [L1], which is exactly the universality claim.