Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.comp_lift_assoc

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

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

7 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory