Theorems · Definition · order theory

LowerAdjoint.closureOperator

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

Every lower adjoint 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

12 results in Mathlib

Foundations

Depth 13 from the axioms · uses propext, Quot.sound

Assumes

PartialOrderPreorder