Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_obj_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) (X_1 : CategoryTheory.Functor J₂ C)
  (X_2 : J₁) {X_3 Y : J₂} (f : X_3 ⟶ Y),
  ((((CategoryTheory.MonoidalCategory.externalProductBifunctorCurried J₁ J₂ C).obj X).obj X_1).obj X_2).map f =
    CategoryTheory.MonoidalCategoryStruct.whiskerLeft (X.obj X_2) (X_1.map f)

Defined in

Mathlib.CategoryTheory.Monoidal.ExternalProduct.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory