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.
Skeletal category and skeleton
Definition
A category is skeletal when isomorphic objects are equal (Isomorphism, groupoid, and connected category).
A skeleton of a category is a full subcategory (Subcategory and full subcategory) that is skeletal and contains an object isomorphic to every object of . Thus a skeleton contains exactly one object from each isomorphism class, once the representative objects have been selected.
Depends on
Used by
- Every monoidal category is monoidally equivalent to a skeletal strict one False statement
- Under the Axiom of Choice, every small category has a skeleton Proposition
- Strictification gives equivalence, not on-the-nose identification Remark
- Strictification itself costs no Choice; choosing a skeleton can Remark
Dependency tree · two levels
5 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
- Emily Riehl, Category Theory in Context, Chapter 1 (standard reference, not scraped)