Theorems · Definition · category theory

CategoryTheory.Functor.functorialityCompPrecompose

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {D : Type u₄} →
          [inst_2 : CategoryTheory.Category.{v₄, u₄} D] →
            {F : CategoryTheory.Functor J C} →
              {H H' : CategoryTheory.Functor C D} →
                (α : H ≅ H') →
                  (CategoryTheory.Limits.Cocone.functoriality F H).comp
                      (CategoryTheory.Limits.Cocone.precompose (F.whiskerLeft α.inv)) ≅
                    CategoryTheory.Limits.Cocone.functoriality F H'

functoriality F _ ⋙ precompose (whiskerLeft F _) simplifies to functoriality F _.

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.CategoryCategoryTheory.Category