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.
Initial object, terminal object, and zero object
Definition
In a category (Category, object, morphism, domain, codomain, identity, composition, and hom-collection), an object is initial when for every object there is exactly one morphism . An object is terminal when for every there is exactly one morphism . These notions are dual under Every theorem about categories has a formal dual obtained by reversing morphisms and composition.
A zero object is an object that is both initial and terminal. The definition does not choose a particular zero object when several distinct but isomorphic ones occur.