DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

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.

Separating and coseparating sets of objects

Definition

Let $C$ be a category. A set $G$ of objects of $C$ is a separating set if, whenever $f, g : X \to Y$ are distinct morphisms, there are $G \in G$ and $h : G \to X$ with $f \circ h \neq g \circ h$ .

A set $H$ of objects is a coseparating set if, whenever $f, g : X \to Y$ are distinct, there are $H \in H$ and $k : Y \to H$ with $k \circ f \neq k \circ g$ . A single object whose singleton family has the relevant property is called a separating or coseparating object.

Separating and coseparating sets of objects

Definition

Depends on

Dependency tree · 2 levels

Sources