A residuated lattice is a lattice (L, ∧, ∨) equipped with a binary operation · (multiplication) and a binary operation → (residuation) satisfying the adjunction: c ≤ (a → b) if and only if (c · a) ≤ b. The residual → is the right adjoint to ·.
Residuated lattices generalize several algebraic structures: Heyting algebras (where · is ∧), quantales, and MV-algebras are all examples. The residuation condition says that multiplication and implication are paired operations — each constrains the other through the order.
In the relationality derivation, the residuation pattern recurs at three levels: implication adjoint to meet (logic), flow adjoint to nucleus (dynamics), and evolution adjoint to measurement (physics). See Residuation in the Derivation for this three-level structure.