Theorems · Definition · category theory

CategoryTheory.Functor.Monoidal.commTensorLeft

{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] →
            (F : CategoryTheory.Functor C D) →
              [F.Monoidal] →
                (X : C) →
                  F.comp (CategoryTheory.MonoidalCategory.tensorLeft (F.obj X)) ≅
                    (CategoryTheory.MonoidalCategory.tensorLeft X).comp F

Monoidal functors commute with left tensoring up to isomorphism

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

4 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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