Theorems · Theorem · category theory
CategoryTheory.IsIso.comp_inv_eq
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (α : Y ⟶ X) [inst_1 : CategoryTheory.IsIso α]
{f : Z ⟶ X} {g : Z ⟶ Y},
CategoryTheory.CategoryStruct.comp f (CategoryTheory.inv α) = g ↔ f = CategoryTheory.CategoryStruct.comp g α- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement · cited by 467
- CategoryTheory.asIso'proof · cited by 8
Cited by13
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invAppproof · cited by 8
- CategoryTheory.GlueData.t_invproof · cited by 6
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturalityproof · cited by 5
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.ofRestrict_invAppproof · cited by 4
- AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_restrictproof · cited by 2
- AlgebraicGeometry.IsOpenImmersion.of_openCover_sourceproof · cited by 1
- IsFreeGroupoid.SpanningTree.loopOfHom_eq_idproof · cited by 1
- CategoryTheory.Adjunction.Triple.leftToRight_eq_counitsproof · cited by 1
- AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓproof · cited by 1
- CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.isNormalEpiCategoryproof · cited by 0
- AlgebraicGeometry.isIso_stalkMap_coprodSpecproof · cited by 0