DefinitionDefinition: AI-adaptedProof: 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.

Coreflective full subcategory and coreflector

Definition

Let $A$ be a full subcategory of $C$ , with inclusion $I : A \to C$ . The subcategory $A$ is coreflective in $C$ when $I$ has a right adjoint $I ⊣ Q, Q : C \to A .$ The functor $Q$ is a coreflector. The counit $ε : I Q \Rightarrow 1_{C}$ is the coreflection counit, and $ε_{C} : I Q (C) \to C$ is the coreflection arrow of $C$ .

This is the categorical dual of Reflective full subcategory and reflector, in the sense of Every theorem about categories has a formal dual obtained by reversing morphisms and composition.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 8 results over 4 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, section 4.5 (standard reference, not scraped)