Theorems · Definition · category theory
CategoryTheory.Iso.symm
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y : C} → (X ≅ Y) → (Y ≅ X)Inverse isomorphism.
- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 993 results in Mathlib
- Foundations
- Depth 15 from the axioms, rests on 91 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
Cited by1,611
Results whose statement or proof uses this declaration.
- CategoryTheory.Equivalence.symmproof · cited by 195
- CategoryTheory.shiftFunctorZeroproof · cited by 82
- CategoryTheory.shiftFunctorCompIsoIdproof · cited by 69
- CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceproof · cited by 61
- CategoryTheory.Functor.asEquivalenceproof · cited by 58
- CategoryTheory.Equivalence.transproof · cited by 57
- CategoryTheory.Equivalence.opproof · cited by 57
- CategoryTheory.IsPushout.isoPushoutproof · cited by 57
- CategoryTheory.shiftFunctorAddproof · cited by 54
- AlgebraicGeometry.Scheme.Hom.appIsoproof · cited by 48
- AlgebraicGeometry.IsAffineOpen.isoSpecproof · cited by 48
- CategoryTheory.Equivalence.congrLeftproof · cited by 46
Showing the 200 most cited of 1,611.