Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.leftUnitor_naturality

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasPushouts C]
  [inst_2 : CategoryTheory.Limits.HasInitial C] [inst_3 : CategoryTheory.CartesianMonoidalCategory C]
  [inst_4 : CategoryTheory.MonoidalClosed C] [inst_5 : CategoryTheory.BraidedCategory C] {X Y : CategoryTheory.Arrow C}
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft
        (CategoryTheory.MonoidalCategoryStruct.tensorUnit (CategoryTheory.Arrow C)) f)
      (CategoryTheory.MonoidalCategoryStruct.leftUnitor Y).hom =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.leftUnitor X).hom f

Defined in

Mathlib.CategoryTheory.Monoidal.Arrow

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.Limits.HasInitialCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.BraidedCategory