DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 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.

Abelian subcategory and exact embedding

Definition

Let $B$ be a full subcategory of an abelian category $A$ . The subcategory $B$ is an abelian subcategory when for every morphism of $B$ its kernel and cokernel computed in $A$ again lie in $B$ , and when $B$ is closed under finite biproducts in $A$ .

An exact embedding is a full embedding (Embedding and full embedding of categories) whose essential image is an abelian subcategory and whose underlying functor is additive (Additive functor).

Abelian subcategory and exact embedding

Definition

Depends on

Dependency tree · 2 levels

Sources