Theorems · Theorem · category theory

CategoryTheory.Arrow.functor_ext

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F G : CategoryTheory.Functor C D},
  (∀ ⦃X Y : C⦄ (f : X ⟶ Y), F.mapArrow.obj (CategoryTheory.Arrow.mk f) = G.mapArrow.obj (CategoryTheory.Arrow.mk f)) →
    F = G

Extensionality lemma for functors C ⥤ D which uses as an assumption that the induced maps Arrow C → Arrow D coincide.

Defined in

Mathlib.CategoryTheory.Comma.Arrow

Cited by

1 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category