Theorems · Theorem · category theory
CategoryTheory.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 : CategoryTheory.NatTrans F G}, α = β → ∀ (X : C), α.app X = β.app X- Defined in
- Mathlib.CategoryTheory.NatTrans
- Cited by
- 58 results in Mathlib
- Foundations
- Depth 14 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 · 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.NatTransstatement and proof · cited by 82
Cited by58
Results whose statement or proof uses this declaration.
- CategoryTheory.Localization.liftNatTrans_appproof · cited by 20
- CategoryTheory.conjugateEquiv_compproof · cited by 7
- CategoryTheory.IsVanKampenColimit.precompose_isIsoproof · cited by 4
- CategoryTheory.ComposableArrows.hom_ext_succproof · cited by 4
- CategoryTheory.Adjunction.Triple.map_rightToLeft_appproof · cited by 4
- CategoryTheory.μ_naturality₂proof · cited by 3
- CategoryTheory.isUniversalColimit_extendCofanproof · cited by 2
- CategoryTheory.Idempotents.whiskeringLeft_obj_preimage_appproof · cited by 2
- CategoryTheory.Triangulated.TStructure.truncLEIsoTruncLT_hom_ι_appproof · cited by 2
- CategoryTheory.Idempotents.app_comp_pproof · cited by 2
- CategoryTheory.Idempotents.app_idemproof · cited by 2
- CategoryTheory.Idempotents.app_p_compproof · cited by 2