Theorems · Theorem · category theory
CategoryTheory.IsIso.hom_inv_id
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) [I : CategoryTheory.IsIso f],
CategoryTheory.CategoryStruct.comp f (CategoryTheory.inv f) = CategoryTheory.CategoryStruct.id X- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 97 results in Mathlib
- Foundations
- Depth 9 from the axioms, rests on 20 definitions · uses Classical.choice
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 · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement · cited by 467
- CategoryTheory.IsIso.outproof · cited by 2
Cited by99
Results whose statement or proof uses this declaration.
- CategoryTheory.asIsoproof · cited by 177
- CategoryTheory.Functor.map_invproof · cited by 38
- CategoryTheory.IsIso.hom_inv_id_assocproof · cited by 29
- CategoryTheory.IsIso.inv_compproof · cited by 22
- RingHom.RespectsIso.cancel_right_isIsoproof · cited by 18
- CategoryTheory.MorphismProperty.cancel_right_of_respectsIsoproof · cited by 16
- CategoryTheory.Bicategory.inv_whiskerLeftproof · cited by 10
- CategoryTheory.IsIso.of_isIso_comp_rightproof · cited by 8
- CategoryTheory.asIso'proof · cited by 8
- CategoryTheory.isIso_of_fully_faithfulproof · cited by 7
- CategoryTheory.Bicategory.inv_whiskerRightproof · cited by 7
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invAppproof · cited by 5