Theorems · Theorem · category theory
CategoryTheory.IsIso.Iso.inv_inv
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ≅ Y), CategoryTheory.inv f.inv = f.hom- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 32,603
- CategoryTheory.Iso.homstatement · cited by 7,684
- CategoryTheory.Iso.invstatement · cited by 6,514
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.invstatement · cited by 467
- CategoryTheory.Iso.inv_hom_idproof · cited by 308
- CategoryTheory.IsIso.inv_eq_of_hom_inv_idproof · cited by 24
Cited by30
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_invproof · cited by 8
- AlgebraicGeometry.SpecMap_ΓSpecIso_homproof · cited by 8
- CategoryTheory.MonoidalCategory.leftUnitor_inv_whiskerRightproof · cited by 7
- CategoryTheory.Bicategory.whiskerLeft_rightUnitor_invproof · cited by 7
- AlgebraicGeometry.Scheme.toSpecΓ_appTopproof · cited by 7
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_appproof · cited by 5
- CategoryTheory.MonoidalCategory.pentagon_invproof · cited by 4
- CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_homproof · cited by 3
- CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_homproof · cited by 3
- CategoryTheory.Bicategory.leftUnitor_inv_whiskerRightproof · cited by 3
- CategoryTheory.Bicategory.pentagon_invproof · cited by 3
- CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp_homproof · cited by 3