Theorems · Theorem · category theory
CategoryTheory.NatIso.isIso_inv_app
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{F G : CategoryTheory.Functor C D} (α : F ⟶ G) [inst_2 : CategoryTheory.IsIso α] (X : C),
(CategoryTheory.inv α).app X = CategoryTheory.inv (α.app X)- Defined in
- Mathlib.CategoryTheory.NatIso
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 24 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.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.NatTrans.appstatement · cited by 7,406
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement · cited by 467
Cited by21
Results whose statement or proof uses this declaration.
- CategoryTheory.Adjunction.Triple.rightToLeft_eq_counitsproof · cited by 2
- CategoryTheory.IsVanKampenColimit.map_reflectiveproof · cited by 2
- SSet.degenerate_iff_of_isIsoproof · cited by 2
- CategoryTheory.Adjunction.Triple.leftToRight_appproof · cited by 2
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_facproof · cited by 2
- CategoryTheory.Adjunction.Triple.rightToLeft_eq_unitsproof · cited by 1
- CategoryTheory.Presheaf.isLeftKanExtension_along_uliftYoneda_iffproof · cited by 1
- CategoryTheory.Adjunction.preservesColimitsOfShape_iffproof · cited by 1
- CategoryTheory.expComparison_evproof · cited by 1
- CategoryTheory.Adjunction.Triple.leftToRight_eq_counitsproof · cited by 1
- CategoryTheory.Adjunction.Triple.leftToRight_opproof · cited by 1