Theorems · Definition · category theory

CategoryTheory.EnrichedFunctor.forgetComp

{W : Type v'} →
  [inst : CategoryTheory.Category.{w', v'} W] →
    [inst_1 : CategoryTheory.MonoidalCategory W] →
      {C : Type u₁} →
        [inst_2 : CategoryTheory.EnrichedCategory W C] →
          {D : Type u₂} →
            [inst_3 : CategoryTheory.EnrichedCategory W D] →
              {E : Type u₃} →
                [inst_4 : CategoryTheory.EnrichedCategory W E] →
                  (F : CategoryTheory.EnrichedFunctor W C D) →
                    (G : CategoryTheory.EnrichedFunctor W D E) →
                      (CategoryTheory.EnrichedFunctor.comp W F G).forget ≅ F.forget.comp G.forget

EnrichedFunctor.forget distributes over composition of enriched functors up to isomorphism.

Defined in

Mathlib.CategoryTheory.Enriched.Basic

Cited by

2 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.EnrichedCategoryCategoryTheory.EnrichedCategoryCategoryTheory.EnrichedCategory