Theorems · Definition · category theory

CategoryTheory.Functor.mapCoconeMapCocone

{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] →
            {E : Type u₅} →
              [inst_3 : CategoryTheory.Category.{v₅, u₅} E] →
                {F : CategoryTheory.Functor J C} →
                  {H : CategoryTheory.Functor C D} →
                    {H' : CategoryTheory.Functor D E} →
                      (c : CategoryTheory.Limits.Cocone F) → H'.mapCocone (H.mapCocone c) ≅ (H.comp H').mapCocone c

The construction mapCocone respects functor composition.

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.CategoryCategoryTheory.Category