Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerLeft_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {D : Type u₁} [inst_2 : CategoryTheory.Category.{v₁, u₁} D] [inst_3 : CategoryTheory.CartesianMonoidalCategory D]
  (F : CategoryTheory.Functor C D) {A B B' : C} (g : B ⟶ B') {Z : D}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj (F.obj A) (F.obj B') ⟶ Z),
  CategoryTheory.CategoryStruct.comp (F.map (CategoryTheory.MonoidalCategoryStruct.whiskerLeft A g))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.prodComparison F A B') h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.prodComparison F A B)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (F.obj A) (F.map g)) h)

Naturality of the prodComparison morphism in the right argument.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory