Theorems · Theorem · category theory

CategoryTheory.congr_fun

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {FC : outParam (C → C → Type u_2)}
  {CC : outParam (C → Type w)} [inst_1 : outParam ((X Y : C) → FunLike (FC X Y) (CC X) (CC Y))]
  [inst_2 : CategoryTheory.ConcreteCategory C FC] {X Y : C} {f g : X ⟶ Y},
  f = g →
    ∀ (x : CategoryTheory.ToType X),
      (CategoryTheory.ConcreteCategory.hom f) x = (CategoryTheory.ConcreteCategory.hom g) x

Analogue of congr_fun h x, when h : f = g is an equality between morphisms in a concrete category.

Defined in

Mathlib.CategoryTheory.ConcreteCategory.Forget

Cited by

10 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryoutParamCategoryTheory.ConcreteCategory