Theorems · Theorem · category theory

CategoryTheory.NatTrans.comp_app_apply

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F G H : CategoryTheory.Functor C D} (α : F ⟶ G) (β : G ⟶ H) (X : C) {F_1 : D → D → Type uF} {carrier : D → Type w}
  {instFunLike : (X Y : D) → FunLike (F_1 X Y) (carrier X) (carrier Y)} [inst_2 : CategoryTheory.ConcreteCategory D F_1]
  (x : carrier (F.obj X)),
  (CategoryTheory.ConcreteCategory.hom ((CategoryTheory.CategoryStruct.comp α β).app X)) x =
    (CategoryTheory.ConcreteCategory.hom (β.app X)) ((CategoryTheory.ConcreteCategory.hom (α.app X)) x)

Defined in

Mathlib.CategoryTheory.Types.Basic

Cited by

4 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.ConcreteCategory