Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_comp

∀ {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 : C) {E : Type u₂} [inst_4 : CategoryTheory.Category.{v₂, u₂} E]
  [inst_5 : CategoryTheory.CartesianMonoidalCategory E] (G : CategoryTheory.Functor D E)
  [inst_6 : CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair A B) F]
  [inst_7 : CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair A B) (F.comp G)]
  [inst_8 : CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair (F.obj A) (F.obj B)) G],
  CategoryTheory.CartesianMonoidalCategory.prodComparisonIso (F.comp G) A B =
    G.mapIso (CategoryTheory.CartesianMonoidalCategory.prodComparisonIso F A B) ≪≫
      CategoryTheory.CartesianMonoidalCategory.prodComparisonIso G (F.obj A) (F.obj B)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.Limits.PreservesLimitCategoryTheory.Limits.PreservesLimitCategoryTheory.Limits.PreservesLimit