Theorems · Theorem · category theory
CategoryTheory.IsIso.eq_inv_of_hom_inv_id
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : X ⟶ Y} [inst_1 : CategoryTheory.IsIso f]
{g : Y ⟶ X}, CategoryTheory.CategoryStruct.comp f g = CategoryTheory.CategoryStruct.id X → g = CategoryTheory.inv f- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement · cited by 467
- CategoryTheory.IsIso.inv_eq_of_hom_inv_idproof · cited by 24
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.map_invproof · cited by 38
- CategoryTheory.Groupoid.inv_eq_invproof · cited by 15
- CategoryTheory.op_invproof · cited by 7
- CategoryTheory.Adjunction.Triple.leftToRight_app_objproof · cited by 4
- CategoryTheory.PrelaxFunctor.map₂_invproof · cited by 4
- CategoryTheory.unop_invproof · cited by 4
- CategoryTheory.GlueData.t'_comp_eq_pullbackSymmetryproof · cited by 1
- CategoryTheory.Functor.LeftLinear.inv_μₗproof · cited by 0
- CategoryTheory.Over.ε_pullback_leftproof · cited by 0
- CategoryTheory.Functor.RightLinear.inv_δᵣproof · cited by 0
- CategoryTheory.Functor.RightLinear.inv_μᵣproof · cited by 0
- CategoryTheory.ObjectProperty.hom_invproof · cited by 0