Theorems · Theorem · category theory

CategoryTheory.AddMonObj.lift_lift_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {A B : C} [inst_2 : CategoryTheory.AddMonObj B] (f g h : A ⟶ B),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CartesianMonoidalCategory.lift
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.lift f g)
          CategoryTheory.AddMonObj.add)
        h)
      CategoryTheory.AddMonObj.add =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CartesianMonoidalCategory.lift f
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.lift g h)
          CategoryTheory.AddMonObj.add))
      CategoryTheory.AddMonObj.add

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

5 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.AddMonObj