Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fst_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  (X Y Z : C) {Z_1 : C} (h : Y ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.SemiCartesianMonoidalCategory.snd X (CategoryTheory.MonoidalCategoryStruct.tensorObj Y Z))
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.fst Y Z) h)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.SemiCartesianMonoidalCategory.fst (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y) Z)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.snd X Y) h)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

1 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory