Theorems · Theorem · category theory
CategoryTheory.NatTrans.isIso_iff_isIso_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} (τ : F ⟶ G), CategoryTheory.IsIso τ ↔ ∀ (X : C), CategoryTheory.IsIso (τ.app X)- Defined in
- Mathlib.CategoryTheory.NatIso
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 25 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 and proof · cited by 7,406
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.NatIso.isIso_of_isIso_appproof · cited by 11
Cited by16
Results whose statement or proof uses this declaration.
- CategoryTheory.Adjunction.isLocalization_leftAdjointproof · cited by 2
- CategoryTheory.Sheaf.isIso_of_coversTopproof · cited by 1
- TopCat.Sheaf.isIso_iff_isIso_basisproof · cited by 1
- CategoryTheory.LocalizerMorphism.isLocalizedEquivalence_of_unit_of_unitproof · cited by 1
- CategoryTheory.Functor.IsRepresentedBy.iff_isIso_uliftYonedaEquivproof · cited by 1
- CategoryTheory.LocalizerMorphism.Derives.isRightDerivedFunctor_of_isIsoproof · cited by 1
- CategoryTheory.ComposableArrows.isIso_iff₁proof · cited by 1
- CategoryTheory.Presheaf.isStrongGeneratorproof · cited by 0
- CategoryTheory.hoFunctor.isIso_prodComparison_of_stdSimplexproof · cited by 0
- AlgebraicGeometry.Scheme.Modules.Hom.isIso_iff_isIso_appproof · cited by 0
- CategoryTheory.Triangulated.TStructure.isIso_eTruncGEIsoGEGEproof · cited by 0