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.
Normal monomorphisms and conormal epimorphisms
Definition
Let be a monomorphism and let be an epimorphism (Monomorphism and epimorphism by left and right cancellation) in a category with zero morphisms and the relevant kernels or cokernels (Kernels and cokernels in a category with zero morphisms as equalizers and coequalizers).
The monomorphism is normal when it is a kernel of some morphism out of . Dually, the epimorphism is conormal when it is a cokernel of some morphism into .
So a normal monomorphism is not merely left-cancellable: it is the inclusion of the part of the codomain killed by a specified morphism. A conormal epimorphism is the dual quotient map.
Depends on
Used by
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Dependency tree · two levels
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Sources
- Junhan Tan, The Freyd-Mitchell Embedding Theorem, Definition 2.2 (standard reference, not scraped)
- Saunders Mac Lane, Categories for the Working Mathematician, VIII.3 (standard reference, not scraped)