Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] {W X Y Z : C} (g : W ⟶ X) (g' : Y ⟶ Z),
  CategoryTheory.CartesianMonoidalCategory.lift
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.snd W Y) g')
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.fst W Y) g) =
    CategoryTheory.CategoryStruct.comp (β_ W Y).hom (CategoryTheory.MonoidalCategoryStruct.tensorHom g' g)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategory