Theorems · Theorem · category theory

CategoryTheory.Dial.associator_hom_F

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasFiniteProducts C]
  [inst_2 : CategoryTheory.Limits.HasPullbacks C] (X Y Z : CategoryTheory.Dial C),
  (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).hom.F =
    CategoryTheory.Limits.prod.lift
      (CategoryTheory.Limits.prod.lift
        (CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.prod.snd CategoryTheory.Limits.prod.fst)
        (CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.prod.snd
          (CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.prod.snd CategoryTheory.Limits.prod.fst)))
      (CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.prod.snd
        (CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.prod.snd CategoryTheory.Limits.prod.snd))

Defined in

Mathlib.CategoryTheory.Dialectica.Monoidal

Cited by

4 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks