Theorems · Theorem · category theory
CategoryTheory.NatTrans.congr_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 β : F ⟶ G}, α = β → ∀ (X : C), α.app X = β.app X- Defined in
- Mathlib.CategoryTheory.Functor.Category
- Cited by
- 119 results in Mathlib
- Foundations
- Depth 20 from the axioms, rests on 101 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
Cited by119
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.descOfIsLeftKanExtension_fac_appproof · cited by 12
- CategoryTheory.NatTrans.shift_app_commproof · cited by 9
- CategoryTheory.IsVanKampenColimit.of_isoproof · cited by 9
- CategoryTheory.shiftFunctorAdd'_assoc_inv_appproof · cited by 6
- CategoryTheory.Functor.liftOfIsRightKanExtension_fac_appproof · cited by 5
- CategoryTheory.shiftFunctorAdd'_zero_add_inv_appproof · cited by 5
- CategoryTheory.Localization.Monoidal.associator_naturalityproof · cited by 5
- CategoryTheory.Functor.pointwiseLeftKanExtension_desc_appproof · cited by 5
- CategoryTheory.Functor.map_shiftFunctorCompIsoId_hom_appproof · cited by 4
- CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_oneproof · cited by 4
- CategoryTheory.shiftFunctorAdd'_add_zero_inv_appproof · cited by 4
- CategoryTheory.shiftFunctorAdd'_assoc_hom_appproof · cited by 3