Theorems · Theorem · category theory

CategoryTheory.ExponentiableMorphism.ev_naturality_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {I J : C} (f : I ⟶ J)
  [inst_1 : CategoryTheory.ChosenPullbacksAlong f] [inst_2 : CategoryTheory.ExponentiableMorphism f]
  {X Y : CategoryTheory.Over I} (g : X ⟶ Y) {Z : CategoryTheory.Over I} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.ChosenPullbacksAlong.pullback f).map
        ((CategoryTheory.ExponentiableMorphism.pushforward f).map g))
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.ExponentiableMorphism.ev f).app Y) h) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.ExponentiableMorphism.ev f).app X)
      (CategoryTheory.CategoryStruct.comp g h)

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlongCategoryTheory.ExponentiableMorphism