Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {X Y Z W : C} (f : X ⟶ Y) (g : X ⟶ Z) (h : X ⟶ W) {Z_1 : C}
  (h_1 : CategoryTheory.MonoidalCategoryStruct.tensorObj Y (CategoryTheory.MonoidalCategoryStruct.tensorObj Z W) ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.CartesianMonoidalCategory.lift f g) h)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator Y Z W).hom h_1) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CartesianMonoidalCategory.lift f (CategoryTheory.CartesianMonoidalCategory.lift g h)) h_1

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

6 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory