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.
The cost of the member calculus
The member calculus uses only the abelian-category primitives already on the page: finite limits and finite colimits, additivity on hom-sets, and one genuinely nonformal stability statement, The pullback of an epimorphism is an epimorphism, which is exactly what makes member equivalence transitive.
What it does not use is equally important: no choice principle, no generator, no projectives, and no smallness assumption. This remark records only those supported proof costs. It does not claim a stronger constructive metatheorem that this run did not source.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
12 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
- Saunders Mac Lane, Categories for the Working Mathematician, VIII.4 (standard reference, not scraped)
- Peter Freyd, Abelian Categories, Chapter 2 (standard reference, not scraped)