DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-11

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.

Pushouts of group homomorphisms

Definition

Given homomorphisms $f : K \to G$ and $h : K \to H$ as in Monoid homomorphism and group homomorphism, a pushout is a group $P$ with homomorphisms $i_{G} : G \to P$ and $i_{H} : H \to P$ such that $i_{G} \circ f = i_{H} \circ h$ , and such that every compatible pair $u : G \to Q$ , $v : H \to Q$ factors through a unique $w : P \to Q$ with $w \circ i_{G} = u$ and $w \circ i_{H} = v$ . The maps $f, h$ need not be injective.

Depends on

Monoid homomorphism and group homomorphism

Pushouts of group homomorphisms

Definition

Depends on

Dependency tree · 2 levels

Sources