DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-29

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.

Member of an object

Definition

Let $A$ be an object of a category. A member of $A$ is simply a morphism with codomain $A$ .

Thus a member is written $x : X \to A,$ and one may read this as " $x$ is a member of $A$ with domain $X$ ". The point of the terminology is that an abelian category need not have honest elements, but it always has arrows into an object.

Depends on

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

Dependency tree · 2 levels

Sources

Saunders Mac Lane, Categories for the Working Mathematician, VIII.4