Theorems · Definition · order theory

GaloisConnection.closureOperator

{α : Type u_1} →
  {β : Type u_4} →
    [inst : PartialOrder α] →
      [inst_1 : Preorder β] → {l : α → β} → {u : β → α} → GaloisConnection l u → ClosureOperator α

Every Galois connection induces a closure operator given by the composition. This is the partial order version of the statement that every adjunction induces a monad.

Defined in

Mathlib.Order.Closure

Cited by

6 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

PartialOrderPreorder