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.
Why the bare phrase 'monoidal functor' is ambiguous across sources
Remark
The term "monoidal functor" is not source-stable. Mac Lane's Chapter XI.2 and the older lax-oriented literature use it for what this page calls a lax monoidal functor. EGNO's Definition 2.4.1 uses it only for the strong case.
For that reason this library does not use the phrase bare. It writes "lax monoidal", "strong monoidal", or "strict monoidal" explicitly, as in Lax, strong, and strict monoidal functors.
Depends on
Used by
- FALSE: every lax monoidal functor has invertible structure maps False statement
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
- S. Mac Lane, Categories for the Working Mathematician, Chapter XI.2 (standard reference, not scraped)
- P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories, Definition 2.4.1 (standard reference, not scraped)