How 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.
The commutative-monoid enrichment of a semiadditive category remains only a sourced remark here
Remark
Every semiadditive category is enriched in commutative monoids. The already-published theorem A category with finite biproducts is enriched in commutative monoids proves this implication, and Semiadditive category records the underlying ordinary notion. The converse needs the additional existence of a zero object and finite biproducts: enrichment in commutative monoids alone only supplies commutative-monoid homs and bilinear composition.
This page keeps that comparison as a remark rather than promoting it to a local theorem, because the present batch's harvested enriched-category sources are Kelly, Riehl, Cruttwell, and the enriched-adjunction appendix, and none of those sources was harvested here as the direct carrier for the full semiadditive/ equivalence.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
6 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
- Saunders Mac Lane, Categories for the Working Mathematician, Chapter VIII.2 (standard reference, not scraped)
- Peter Freyd, Abelian Categories, Exercise 2A.2 (standard reference, not scraped)