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.

Monomorphism and epimorphism by left and right cancellation

Definition

Let $f : A \to B$ be a morphism in a category (Category, object, morphism, domain, codomain, identity, composition, and hom-collection).

$f$ is a monomorphism, or monic, when $f \circ g = f \circ h$ implies $g = h$ for every parallel pair $g, h : X \to A$ .
$f$ is an epimorphism, or epic, when $g \circ f = h \circ f$ implies $g = h$ for every parallel pair $g, h : B \to Y$ .

Thus monomorphisms are left-cancellable and epimorphisms are right-cancellable. The definitions are formally dual.

Depends on

Category, object, morphism, domain, codomain, identity, composition, and hom-collection

Dependency tree · 2 levels

Sources

Emily Riehl, Category Theory in Context, Chapter 1