Theorems · Theorem · category theory

CategoryTheory.comp_apply

∀ {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 Z : C}
  (f : X ⟶ Y) (g : Y ⟶ Z) (x : CategoryTheory.ToType X),
  (CategoryTheory.ConcreteCategory.hom (CategoryTheory.CategoryStruct.comp f g)) x =
    (CategoryTheory.ConcreteCategory.hom g) ((CategoryTheory.ConcreteCategory.hom f) x)

Defined in

Mathlib.CategoryTheory.ConcreteCategory.Basic

Cited by

387 results in Mathlib

Foundations

Depth 6 from the axioms, rests on 18 definitions · uses propext

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory