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.
Mac Lane's warning about left and right Kan extensions
Remarks
Mac Lane warns in Chapter X.3 that some authors reverse the names. This library follows Left and right Kan extensions: a left Kan extension comes with a unit , and a right Kan extension comes with a counit .
Nothing mathematical changes with the vocabulary, but the directions of the two structure maps do. This page therefore keeps those arrows visible in every definition and theorem rather than writing only and .
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
4 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
- S. Mac Lane, Categories for the Working Mathematician, 2nd ed., Chapter X.3 (standard reference, not scraped)