Theorems · Definition · category theory

CategoryTheory.Equivalence.monoidalOfPrecompFunctor

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      {D : Type u₂} →
        [inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
          [inst_3 : CategoryTheory.MonoidalCategory D] →
            {E : Type u₃} →
              [inst_4 : CategoryTheory.Category.{v₃, u₃} E] →
                [inst_5 : CategoryTheory.MonoidalCategory E] →
                  (e : C ≌ D) →
                    (F : CategoryTheory.Functor D E) →
                      {F' : CategoryTheory.Functor C E} →
                        (e.functor.comp F ≅ F') → [e.inverse.Monoidal] → [F'.Monoidal] → F.Monoidal

Given a functor F and an equivalence of categories e such that e.inverse and e.functor ⋙ F are monoidal functors, F is monoidal as well.

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.MonoidalCategoryTheory.Functor.Monoidal