Theorems · Definition · category theory
CategoryTheory.Iso.unop
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : Cᵒᵖ} → (X ≅ Y) → (Opposite.unop Y ≅ Opposite.unop X)The isomorphism obtained from an isomorphism in the opposite category.
- Defined in
- Mathlib.CategoryTheory.Opposites
- Cited by
- 33 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.
Cites7
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 and proof · 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
- Opposite.unopstatement · cited by 2,231
- Quiver.Hom.unopproof · cited by 903
Cited by59
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.HomologyData.unopproof · cited by 6
- HomologicalComplex.truncLE'XIsoproof · cited by 4
- CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.isoproof · cited by 4
- CategoryTheory.kernelUnopUnopproof · cited by 3
- CategoryTheory.Iso.unop_invstatement and proof · cited by 3
- CategoryTheory.Functor.isTriangulated_of_opproof · cited by 2
- CategoryTheory.cokernelUnopUnopproof · cited by 2
- CategoryTheory.ObjectProperty.op_isoClosureproof · cited by 2
- HomologicalComplex.truncLE'XIsoCyclesproof · cited by 2
- CategoryTheory.isoOpEquivproof · cited by 2
- CategoryTheory.Pretriangulated.Opposite.mem_distinguishedTriangles_iff'proof · cited by 2
- CategoryTheory.ProjectiveResolution.isoExtproof · cited by 1