Theorems · Theorem · category theory

CategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc

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