Theorems · Definition · category theory
CategoryTheory.Groupoid.invEquivalence
(C : Type u) → [inst : CategoryTheory.Groupoid C] → C ≌ Cᵒᵖ
The equivalence from a groupoid C to its opposite sending every morphism to its inverse.
- Defined in
- Mathlib.CategoryTheory.Groupoid
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Groupoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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.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.Groupoidstatement and proof · cited by 182
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.closedIhomproof · cited by 9
- CategoryTheory.Groupoid.invEquivalence_inverse_mapstatement and proof · cited by 0
- CategoryTheory.Groupoid.invEquivalence_inverse_objstatement and proof · cited by 0
- CategoryTheory.Groupoid.invEquivalence_unitIsostatement and proof · cited by 0
- CategoryTheory.Functor.closedIhom_map_appstatement · cited by 0
- CategoryTheory.Functor.closedIhom_obj_mapstatement · cited by 0
- CategoryTheory.Groupoid.invEquivalence_counitIsostatement and proof · cited by 0
- CategoryTheory.Groupoid.invEquivalence_functor_mapstatement and proof · cited by 0
- CategoryTheory.Groupoid.invEquivalence_functor_objstatement and proof · cited by 0