Theorems · Theorem · category theory

CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.ChosenPullbacks C] {X : C}
  (R S T : CategoryTheory.Over X) {Z : C} (h : T.left ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Over.Hom.left (CategoryTheory.MonoidalCategoryStruct.associator R S T).hom)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.ChosenPullbacksAlong.snd R.hom
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.ChosenPullbacksAlong.snd S.hom T.hom) T.hom))
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.ChosenPullbacksAlong.snd S.hom T.hom) h)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ChosenPullbacksAlong.snd (CategoryTheory.MonoidalCategoryStruct.tensorObj R S).hom T.hom) h

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.Over

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacks