Theorems · Theorem · category theory

CategoryTheory.Functor.map_comp_apply

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (self : CategoryTheory.Functor C D) {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) {F : D → D → Type uF} {carrier : D → Type w}
  {instFunLike : (X Y : D) → FunLike (F X Y) (carrier X) (carrier Y)} [inst_2 : CategoryTheory.ConcreteCategory D F]
  (x : carrier (self.obj X)),
  (CategoryTheory.ConcreteCategory.hom (self.map (CategoryTheory.CategoryStruct.comp f g))) x =
    (CategoryTheory.ConcreteCategory.hom (self.map g)) ((CategoryTheory.ConcreteCategory.hom (self.map f)) x)

Defined in

Mathlib.CategoryTheory.Types.Basic

Cited by

26 results in Mathlib

Foundations

Depth 7 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.ConcreteCategory