DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-28

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.

A category with enough projectives and with enough injectives

An abelian category has enough projectives when every object $A$ admits an epimorphism $P ↠ A$ with $P$ projective (Projective object).

It has enough injectives when every object $A$ admits a monomorphism $A ↣ I$ with $I$ injective (Injective object).

Depends on