Theorems · Theorem · category theory

CategoryTheory.eqToHom_map_comp_apply

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) {X Y Z : C} (p : X = Y) (q : Y = Z) {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 (F.map (CategoryTheory.eqToHom q)))
      ((CategoryTheory.ConcreteCategory.hom (F.map (CategoryTheory.eqToHom p))) x) =
    (CategoryTheory.ConcreteCategory.hom (F.map (CategoryTheory.eqToHom ⋯))) x

Defined in

Mathlib.CategoryTheory.Types.Basic

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.ConcreteCategory