Theorems · Definition · category theory
CategoryTheory.WithInitial.opEquiv
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] → (CategoryTheory.WithInitial C)ᵒᵖ ≌ CategoryTheory.WithTerminal CᵒᵖThe opposite category of WithInitial C is equivalent to WithTerminal Cᵒᵖ.
- Cited by
- 20 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 by21
Results whose statement or proof uses this declaration.
- AugmentedSimplexCategory.equivAugmentedSimplicialObjectproof · cited by 23
- AugmentedSimplexCategory.equivAugmentedSimplicialObject_unitIso_inv_app_appstatement and proof · cited by 0
- CategoryTheory.WithInitial.opEquiv_counitIso_hom_appstatement and proof · cited by 0
- CategoryTheory.WithInitial.opEquiv_counitIso_inv_appstatement and proof · cited by 0
- CategoryTheory.WithInitial.opEquiv_functor_mapstatement and proof · cited by 0
- CategoryTheory.WithInitial.opEquiv_functor_objstatement and proof · cited by 0
- CategoryTheory.WithInitial.opEquiv_inverse_mapstatement and proof · cited by 0
- CategoryTheory.WithInitial.opEquiv_inverse_objstatement and proof · cited by 0
- CategoryTheory.WithInitial.opEquiv_unitIso_hom_appstatement and proof · cited by 0
- CategoryTheory.WithInitial.opEquiv_unitIso_inv_appstatement and proof · cited by 0
- AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_left_appstatement and proof · cited by 0
- AugmentedSimplexCategory.equivAugmentedSimplicialObject_counitIso_hom_app_rightstatement and proof · cited by 0