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.
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.
The pullback of an epimorphism is an epimorphism (The pullback of an epimorphism is an epimorphism).
Proof
Take any epimorphism and any pullback of it.
The pullback leg is epic by [L1], which is exactly the universality claim.
Depends on
Used by
Dependency tree · two levels
6 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
- The Stacks Project, Section 12.5, Lemma 12.5.14 (standard reference, not scraped)