Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.inv_hom_id_tensor_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {V W X Y Z : C}
  (f : V ≅ W) (g : X ⟶ Y) (h : Y ⟶ Z) {Z_1 : C} (h_1 : CategoryTheory.MonoidalCategoryStruct.tensorObj W Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom f.inv g)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom f.hom h) h_1) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.CategoryStruct.id W) g)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.CategoryStruct.id W) h) h_1)

Defined in

Mathlib.CategoryTheory.Monoidal.Category

Cited by

0 results in Mathlib

Foundations

Depth 9 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory