Theorems · Definition · category theory

CategoryTheory.leftDualIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      {X₁ X₂ Y : C} → CategoryTheory.ExactPairing X₁ Y → CategoryTheory.ExactPairing X₂ Y → (X₁ ≅ X₂)

Left duals are isomorphic.

Defined in: Mathlib.CategoryTheory.Monoidal.Rigid.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.ExactPairingstatement and proof · cited by 20
CategoryTheory.leftAdjointMateproof · cited by 13

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.leftDualIso_idstatement · cited by 0
CategoryTheory.leftDualTensorIsoproof · cited by 0