Theorems · Definition · category theory
CategoryTheory.prodOpEquiv
(C : Type u₃) →
[inst : CategoryTheory.Category.{v₃, u₃} C] →
{D : Type u₄} → [inst_1 : CategoryTheory.Category.{v₄, u₄} D] → (C × D)ᵒᵖ ≌ Cᵒᵖ × DᵒᵖThe equivalence between the opposite of a product and the product of the opposites.
- Defined in
- Mathlib.CategoryTheory.Products.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Quiver.Homproof · cited by 32,603
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Functor.idproof · cited by 3,333
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.opproof · cited by 1,948
- Quiver.Hom.unopproof · cited by 903
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Prod.mkHomproof · cited by 108
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.prodOpEquiv_counitIso_hom_appstatement and proof · cited by 0
- CategoryTheory.prodOpEquiv_counitIso_inv_appstatement and proof · cited by 0
- CategoryTheory.prodOpEquiv_functor_mapstatement and proof · cited by 0
- CategoryTheory.prodOpEquiv_functor_objstatement and proof · cited by 0
- CategoryTheory.prodOpEquiv_inverse_mapstatement and proof · cited by 0
- CategoryTheory.prodOpEquiv_inverse_objstatement and proof · cited by 0
- CategoryTheory.prodOpEquiv_unitIso_hom_appstatement and proof · cited by 0
- CategoryTheory.prodOpEquiv_unitIso_inv_appstatement and proof · cited by 0