Theorems · Definition · category theory

CategoryTheory.Equivalence.leftOp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → (C ≌ Dᵒᵖ) → (Cᵒᵖ ≌ D)

An equivalence between C and Dᵒᵖ gives an equivalence between Cᵒᵖ and D.

Defined in: Mathlib.CategoryTheory.Opposites
Cited by: 8 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category

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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
Oppositestatement and proof · cited by 8,081
CategoryTheory.Equivalencestatement and proof · cited by 601
CategoryTheory.Equivalence.transproof · cited by 57
CategoryTheory.Equivalence.opproof · cited by 57
CategoryTheory.opOpEquivalenceproof · cited by 34

Cited by8

Results whose statement or proof uses this declaration.

CategoryTheory.Equivalence.leftOp_counitIso_hom_appstatement · cited by 0
CategoryTheory.Equivalence.leftOp_counitIso_inv_appstatement · cited by 0
CategoryTheory.Equivalence.leftOp_functor_mapstatement and proof · cited by 0
CategoryTheory.Equivalence.leftOp_functor_objstatement and proof · cited by 0
CategoryTheory.Equivalence.leftOp_inverse_mapstatement and proof · cited by 0
CategoryTheory.Equivalence.leftOp_inverse_objstatement and proof · cited by 0
CategoryTheory.Equivalence.leftOp_unitIso_hom_appstatement · cited by 0
CategoryTheory.Equivalence.leftOp_unitIso_inv_appstatement · cited by 0