Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.whiskerLeftIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasPushouts C] →
      [inst_2 : CategoryTheory.MonoidalCategory C] →
        (X₁ X₂ : CategoryTheory.Arrow C) →
          {W : C} →
            [CategoryTheory.Limits.PreservesColimit
                  (CategoryTheory.Limits.span (CategoryTheory.MonoidalCategoryStruct.whiskerRight X₁.hom X₂.left)
                    (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X₁.left X₂.hom))
                  (CategoryTheory.MonoidalCategory.tensorLeft W)] →
              CategoryTheory.Arrow.mk (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W (X₁ □ X₂).hom) ≅
                CategoryTheory.Arrow.mk (CategoryTheory.MonoidalCategoryStruct.whiskerLeft W X₁.hom) □ X₂

Left-whiskering the pushout-product of X₁ and X₂ with W : C is isomorphic to the pushout-product of W ◁ X₁ and X₂.

Defined in

Mathlib.CategoryTheory.Monoidal.PushoutProduct

Cited by

5 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.MonoidalCategoryCategoryTheory.Limits.PreservesColimit