Theorems · Theorem · category theory

CategoryTheory.ConcreteCategory.congr_hom

∀ {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},
  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.Basic

Cited by

138 results in Mathlib

Foundations

Depth 5 from the axioms, rests on 15 definitions · uses no axioms

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory