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.
Unbracketed tensor strings are not yet defined on this page
Remark
Before coherence is proved, an unbracketed expression with has no meaning by itself on this page. A two-fold product is already defined by the tensor bifunctor; for three or more factors, what is defined is a parenthesised tensor word and its evaluation functor from Parenthesised tensor words and their evaluation functors.
So later pages that write an unbracketed string must depend on the coherence page that licenses suppressing the parentheses. On the present page, every triple or longer tensor expression is written with its brackets shown.
Depends on
Used by
Dependency tree · two levels
2 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, Chapter VII.2 (standard reference, not scraped)
- P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories, Chapter 2.9 (standard reference, not scraped)