DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-08-27

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.

Semiadditive category

Definition

A category is semiadditive when it has all finite biproducts (Biproduct). Equivalently, it has a zero object (The empty biproduct is a zero object) and binary biproducts, and then each hom-set carries the canonical commutative-monoid structure of A category with finite biproducts is enriched in commutative monoids.

Depends on

Used by

A zero kernel does not force monicity in a merely semiadditive category Counterexample
Commutative monoids are semiadditive and not additive Counterexample
A semiadditive category is preadditive exactly when every morphism has an additive inverse Theorem

Dependency tree · two levels

8 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, Definition 2.1 (standard reference, not scraped)