Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.externalProductBifunctorCurried_obj_map_app_app

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

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