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.
FALSE: the addition on an additive category is extra structure that must be chosen
Statement
False claim: the addition on an additive category is extra structure that must be chosen independently of the biproduct data.
Facts & Assumptions
Given: An additive category.
An additive category has finite biproducts (Additive category).
The commutative-monoid enrichment determined by finite biproducts is unique (The commutative-monoid enrichment of a category with finite biproducts is unique).
Refutation
By [L1], an additive category has exactly the finite biproduct structure to which [L2] applies.
The theorem [L2] says that any compatible addition law on the hom-sets is forced by that biproduct structure. So there is no further independent choice to make.
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
- Merlin Christ, Tobias Dyckerhoff, and Tashi Walde, Lax Additivity, Section 2 (standard reference, not scraped)