Theorems · Definition · category theory

CategoryTheory.Limits.Cocone.precomposeComp

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F G H : CategoryTheory.Functor J C} →
          (β : H ⟶ G) →
            (α : G ⟶ F) →
              CategoryTheory.Limits.Cocone.precompose (CategoryTheory.CategoryStruct.comp β α) ≅
                (CategoryTheory.Limits.Cocone.precompose α).comp (CategoryTheory.Limits.Cocone.precompose β)

Precomposing a cocone by the composite natural transformation α ≫ β is the same as precomposing by β and then by α.

Defined in

Mathlib.CategoryTheory.Limits.Cones

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category