Theorems · Theorem · category theory
CategoryTheory.op_inv
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y) [inst_1 : CategoryTheory.IsIso f],
(CategoryTheory.inv f).op = CategoryTheory.inv f.op- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 16 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.Homstatement and proof · cited by 32,603
- Oppositestatement · cited by 8,081
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- Quiver.Hom.opstatement and proof · cited by 1,948
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement · cited by 467
- CategoryTheory.IsIso.inv_hom_idproof · cited by 88
- CategoryTheory.op_compproof · cited by 72
- CategoryTheory.IsIso.eq_inv_of_hom_inv_idproof · cited by 17
- CategoryTheory.op_idproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.toSpecΓ_appTopproof · cited by 7
- AlgebraicGeometry.Spec.map_invproof · cited by 3
- CategoryTheory.MorphismProperty.RightFraction.op_mapproof · cited by 2
- CategoryTheory.Presieve.isSheafFor_pullback_iffproof · cited by 1
- CategoryTheory.Adjunction.Triple.op_rightToLeftproof · cited by 1
- CategoryTheory.Adjunction.Triple.leftToRight_opproof · cited by 1
- CategoryTheory.MorphismProperty.LeftFraction.op_mapproof · cited by 0