Theorems · Theorem · category theory

CategoryTheory.ConcreteCategory.hom_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type w}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC] {X Y : C}
  (f g : X ⟶ Y),
  (∀ (x : CC X), (CategoryTheory.ConcreteCategory.hom f) x = (CategoryTheory.ConcreteCategory.hom g) x) → f = g

In any concrete category, we can test equality of morphisms by pointwise evaluations.

Defined in

Mathlib.CategoryTheory.ConcreteCategory.Basic

Cited by

48 results in Mathlib

Foundations

Depth 18 from the axioms · uses Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory