Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_natural_whiskerLeft

∀ {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}
  [inst_4 : CategoryTheory.IsIso (CategoryTheory.CartesianMonoidalCategory.prodComparison F A B)] (g : B ⟶ B')
  [inst_5 : CategoryTheory.IsIso (CategoryTheory.CartesianMonoidalCategory.prodComparison F A B')],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.inv (CategoryTheory.CartesianMonoidalCategory.prodComparison F A B))
      (F.map (CategoryTheory.MonoidalCategoryStruct.whiskerLeft A g)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (F.obj A) (F.map g))
      (CategoryTheory.inv (CategoryTheory.CartesianMonoidalCategory.prodComparison F A B'))

If the product comparison morphism is an iso, its inverse is natural in the right argument.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.IsIsoCategoryTheory.IsIso