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.

Adjoint triple $L ⊣ M ⊣ R$

Definition

An adjoint triple $L ⊣ M ⊣ R$ consists of categories $C, D$ , functors

$L, R : D \to C, M : C \to D,$

and adjunctions $L ⊣ M$ and $M ⊣ R$ in the sense of Adjunction by unit, counit, and the triangle identities. Thus the middle functor is simultaneously a right adjoint and a left adjoint, with separate units and counits for the two adjunctions.

Depends on

Adjunction by unit, counit, and the triangle identities

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 6 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

Emily Riehl, Category Theory in Context, 2nd ed., Section 4.1 (standard reference, not scraped)

Adjoint triple L⊣M⊣RL⊣M⊣R