Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.leftUnitor

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasPushouts C] →
      [inst_2 : CategoryTheory.CartesianMonoidalCategory C] →
        [CategoryTheory.MonoidalClosed C] →
          [inst_4 : CategoryTheory.Limits.HasInitial C] →
            [CategoryTheory.BraidedCategory C] →
              (X : CategoryTheory.Arrow C) →
                (CategoryTheory.Arrow.mk
                      (CategoryTheory.Limits.initial.to (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)) □
                    X) ≅
                  X

If C is a braided CCC with pushouts and an initial object, then (⊥_ C ⟶ 𝟙_ C) □ X ≅ X.

Defined in

Mathlib.CategoryTheory.Monoidal.PushoutProduct

Cited by

1 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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