DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge 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.

The solution-set condition for a functor, stated object by object

Definition

Let $U : A \to C$ be a functor and fix an object $C \in C$ . The functor $U$ satisfies the solution-set condition at $C$ if there is a supplied set-indexed family of arrows $η_{i} : C \to U (A_{i}) (i \in I)$ such that every arrow $f : C \to U (A)$ factors through one of them: for some $i \in I$ and some $h : A_{i} \to A$ , $f = U (h) \circ η_{i} .$ The functor satisfies the solution-set condition if it satisfies this condition at every object $C$ . An assertion of the condition object by object supplies no simultaneous choice of a solution family over a proper class of objects.

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 9 results over 5 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

E. Riehl, Category Theory in Context, theorem 4.7.3 (standard reference, not scraped)
T. Leinster, Basic Category Theory, theorem 6.3.10 (standard reference, not scraped)