Theorems · Definition · category theory
CategoryTheory.Join.opEquiv
(C : Type u₁) →
(D : Type u₂) →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] → (CategoryTheory.Join C D)ᵒᵖ ≌ CategoryTheory.Join Dᵒᵖ CᵒᵖThe equivalence (C ⋆ D)ᵒᵖ ≌ Dᵒᵖ ⋆ Cᵒᵖ induced by Join.opEquivFunctor and
Join.opEquivInverse.
- Defined in
- Mathlib.CategoryTheory.Join.Opposites
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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.Functor.objproof · cited by 19,642
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Isoproof · cited by 3,963
- CategoryTheory.Functor.idproof · cited by 3,333
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.Functor.opproof · cited by 997
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Functor.rightOpproof · cited by 214
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.Join.inclLeftCompOpEquivInversestatement · cited by 2
- CategoryTheory.Join.inclRightCompOpEquivInversestatement · cited by 2
- CategoryTheory.Join.InclLeftCompRightOpOpEquivFunctorstatement · cited by 2
- CategoryTheory.Join.InclRightCompRightOpOpEquivFunctorstatement · cited by 2
- CategoryTheory.Join.opEquiv_functor_map_op_edgestatement · cited by 0
- CategoryTheory.Join.opEquiv_functor_map_op_inclLeftstatement · cited by 0
- CategoryTheory.Join.opEquiv_functor_map_op_inclRightstatement · cited by 0
- CategoryTheory.Join.opEquiv_functor_obj_op_leftstatement · cited by 0
- CategoryTheory.Join.opEquiv_functor_obj_op_rightstatement · cited by 0
- CategoryTheory.Join.opEquiv_inverse_map_edge_opstatement · cited by 0
- CategoryTheory.Join.opEquiv_inverse_map_inclLeft_opstatement · cited by 0
- CategoryTheory.Join.opEquiv_inverse_map_inclRight_opstatement · cited by 0