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.
Every monoidal category is monoidally equivalent to a skeletal strict one
Statement
False claim: every monoidal category is monoidally equivalent to a strict monoidal category that is also skeletal.
Facts & Assumptions
Given: The meaning of skeletal category and the scope warning about strictification.
A skeletal category is one in which isomorphic objects are equal (Skeletal category and skeleton).
The strictification remark records that one cannot in general ask for a model that is both strict and skeletal at once (Strictification gives equivalence, not on-the-nose identification).
Refutation
By [L1], adding the word "skeletal" strengthens the strictification target by requiring equality of all isomorphic objects there.
But [L2] states that this stronger simultaneous requirement can fail even though ordinary strictification succeeds.
Hence the claim is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
7 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
- P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories, Remark 2.8.7 (standard reference, not scraped)