Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.externalProductBifunctor

(J₁ : Type u₁) →
  (J₂ : Type u₂) →
    (C : Type u₃) →
      [inst : CategoryTheory.Category.{v₁, u₁} J₁] →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} J₂] →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            [CategoryTheory.MonoidalCategory C] →
              CategoryTheory.Functor (CategoryTheory.Functor J₁ C × CategoryTheory.Functor J₂ C)
                (CategoryTheory.Functor (J₁ × J₂) C)

The external product bifunctor: given diagrams K₁ : J₁ ⥤ C and K₂ : J₂ ⥤ C, this is the bifunctor (j₁, j₂) ↦ K₁ j₁ ⊗ K₂ j₂.

Defined in

Mathlib.CategoryTheory.Monoidal.ExternalProduct.Basic

Cited by

9 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory