Theorems · Theorem · category theory
CategoryTheory.IsIso.Iso.inv_hom
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ≅ Y), CategoryTheory.inv f.hom = f.inv- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 15 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_inv_hom_idproof · cited by 3
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_invproof · cited by 8
- CategoryTheory.Bicategory.whiskerLeft_rightUnitor_invproof · cited by 7
- CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_homproof · cited by 3
- CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_inv_homproof · cited by 2
- CategoryTheory.BraidedCategory.braiding_tensor_left_invproof · cited by 2
- CategoryTheory.MonoidalCategory.pentagon_inv_hom_hom_hom_invproof · cited by 2
- CategoryTheory.BraidedCategory.braiding_tensor_right_invproof · cited by 2
- CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_invproof · cited by 2
- CategoryTheory.Functor.congr_inv_of_congr_homproof · cited by 1
- CategoryTheory.Bicategory.pentagon_inv_inv_hom_inv_invproof · cited by 1
- CategoryTheory.MonoidalCategory.pentagon_hom_hom_inv_hom_homproof · cited by 1
- CategoryTheory.Bicategory.pentagon_hom_hom_inv_hom_homproof · cited by 1