Theorems · Theorem · category theory

CategoryTheory.Monoidal.InducingFunctorData.tensorHom_eq

∀ {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.MonoidalCategoryStruct D]
  {F : CategoryTheory.Functor D C} (self : CategoryTheory.Monoidal.InducingFunctorData F) {X₁ Y₁ X₂ Y₂ : D}
  (f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂),
  F.map (CategoryTheory.MonoidalCategoryStruct.tensorHom f g) =
    CategoryTheory.CategoryStruct.comp (self.μIso X₁ X₂).inv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom (F.map f) (F.map g))
        (self.μIso Y₁ Y₂).hom)

Defined in

Mathlib.CategoryTheory.Monoidal.Transport

Cited by

0 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryStruct