Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.isInitialIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasPushouts C] →
      [inst_2 : CategoryTheory.CartesianMonoidalCategory C] →
        [CategoryTheory.MonoidalClosed C] →
          (X : CategoryTheory.Arrow C) →
            {I : C} →
              (i : CategoryTheory.Limits.IsInitial I) →
                {W : C} →
                  (X □ CategoryTheory.Arrow.mk (i.to W)) ≅
                    CategoryTheory.Arrow.mk (CategoryTheory.MonoidalCategoryStruct.whiskerRight X.hom W)

The arrow isomorphism X □ (∅ ⟶ W) ≅ X ▷ W in a CCC with pushouts and an initial object.

Defined in

Mathlib.CategoryTheory.Monoidal.PushoutProduct

Cited by

4 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonoidalClosed