Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.externalProductBifunctor_obj_map

∀ (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]
  [inst_3 : CategoryTheory.MonoidalCategory C] (X : CategoryTheory.Functor J₁ C × CategoryTheory.Functor J₂ C)
  {X_1 Y : J₁ × J₂} (f : X_1 ⟶ Y),
  ((CategoryTheory.MonoidalCategory.externalProductBifunctor J₁ J₂ C).obj X).map f =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight (X.1.map f.1) (X.2.obj X_1.2))
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (X.1.obj Y.1) (X.2.map f.2))

Defined in

Mathlib.CategoryTheory.Monoidal.ExternalProduct.Basic

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory