Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.Arrow.PullbackHom.isInitialIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasPullbacks C] →
      [inst_2 : CategoryTheory.CartesianMonoidalCategory C] →
        [inst_3 : CategoryTheory.MonoidalClosed C] →
          [CategoryTheory.BraidedCategory C] →
            (X : CategoryTheory.Arrow C) →
              {I : C} →
                (i : CategoryTheory.Limits.IsInitial I) →
                  {W : C} →
                    (Opposite.op (CategoryTheory.Arrow.mk (i.to W)) ⋔ X) ≅
                      CategoryTheory.Arrow.mk ((CategoryTheory.ihom W).map X.hom)

The arrow isomorphism (∅ ⟶ W) ⋔ (f : A ⟶ B) ≅ (W ⟹ A ⟶ W ⟹ B) in a braided CCC with pullbacks and an initial object.

Defined in

Mathlib.CategoryTheory.Monoidal.PushoutProduct

Cited by

4 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.BraidedCategory