Theorems · Definition · category theory
CategoryTheory.Iso.op
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : C} → (X ≅ Y) → (Opposite.op Y ≅ Opposite.op X)The opposite isomorphism.
- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
- Quiver.Hom.opproof · cited by 1,948
Cited by104
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.isoSpecproof · cited by 48
- AlgebraicGeometry.Scheme.Opens.topIsoproof · cited by 20
- CategoryTheory.Functor.leftOpRightOpEquivproof · cited by 15
- CategoryTheory.Iso.op_homstatement and proof · cited by 13
- CategoryTheory.Iso.op_invstatement and proof · cited by 10
- CategoryTheory.CategoryOfElements.costructuredArrowYonedaEquivalenceproof · cited by 9
- AlgebraicGeometry.IsOpenImmersion.ΓIsoproof · cited by 8
- CategoryTheory.ShortComplex.HomologyData.opproof · cited by 7
- AlgebraicGeometry.AffineSpace.SpecIsoproof · cited by 7
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeObjIsoproof · cited by 6
- CategoryTheory.imageUnopOpproof · cited by 6