Theorems · Definition · category theory
CategoryTheory.WithTerminal.opEquiv
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] → (CategoryTheory.WithTerminal C)ᵒᵖ ≌ CategoryTheory.WithInitial CᵒᵖThe opposite category of WithTerminal C is equivalent to WithInitial Cᵒᵖ.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- 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.Iso.reflproof · cited by 727
- CategoryTheory.Equivalencestatement · cited by 601
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.WithTerminal.opEquiv_counitIso_hom_appstatement and proof · cited by 0
- CategoryTheory.WithTerminal.opEquiv_counitIso_inv_appstatement and proof · cited by 0
- CategoryTheory.WithTerminal.opEquiv_functor_mapstatement and proof · cited by 0
- CategoryTheory.WithTerminal.opEquiv_functor_objstatement and proof · cited by 0
- CategoryTheory.WithTerminal.opEquiv_inverse_mapstatement and proof · cited by 0
- CategoryTheory.WithTerminal.opEquiv_inverse_objstatement and proof · cited by 0
- CategoryTheory.WithTerminal.opEquiv_unitIso_hom_appstatement and proof · cited by 0
- CategoryTheory.WithTerminal.opEquiv_unitIso_inv_appstatement and proof · cited by 0