DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

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.

k-linear categories and k-linear functors

Definition

Let $k$ be a field. A $k$ -linear category is a category $C$ for which every ${Hom}_{C} (X, Y)$ is a $k$ -vector space and composition is $k$ -bilinear. A functor $F : C \to D$ between $k$ -linear categories is $k$ -linear if each induced map on hom-spaces is $k$ -linear.

Depends on

Used by

Locally finite k-linear abelian categories Definition

Dependency tree · two levels

11 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

Etingof, Gelaki, Nikshych, Ostrik, Tensor Categories, Definitions 1.2.2–1.2.3 (standard reference, not scraped)