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.
Abelian subcategory and exact embedding
Definition
Let be a full subcategory of an abelian category . The subcategory is an abelian subcategory when for every morphism of its kernel and cokernel computed in again lie in , and when is closed under finite biproducts in .
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).
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Barry Mitchell, Theory of Categories, Chapter I (standard reference, not scraped)
- Peter Freyd, Abelian Categories, Chapter 7 (standard reference, not scraped)