Theorems · Theorem · category theory
CategoryTheory.IsIso.inv_hom_id_assoc
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) [I : CategoryTheory.IsIso f] {Z : C}
(h : Y ⟶ Z), CategoryTheory.CategoryStruct.comp (CategoryTheory.inv f) (CategoryTheory.CategoryStruct.comp f h) = h- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Category.assocproof · cited by 6,433
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement and proof · cited by 467
- CategoryTheory.IsIso.inv_hom_idproof · cited by 88
Cited by37
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.cancel_left_of_respectsIsoproof · cited by 33
- RingHom.RespectsIso.cancel_left_isIsoproof · cited by 6
- CategoryTheory.GlueData.t_invproof · cited by 6
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_invAppproof · cited by 5
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturalityproof · cited by 5
- CategoryTheory.IsVanKampenColimit.precompose_isIso_iffproof · cited by 4
- AlgebraicGeometry.IsClosedImmersion.lift_facproof · cited by 4
- CategoryTheory.IsPullback.of_horiz_isIso_monoproof · cited by 4
- AlgebraicGeometry.Scheme.Hom.ker_comp_of_isIsoproof · cited by 4
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift_facproof · cited by 3
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernelproof · cited by 3
- CategoryTheory.Pretriangulated.isIso₂_of_isIso₁₃proof · cited by 3