Theorems · Theorem · category theory

CategoryTheory.ExponentiableMorphism.pushforwardId_hom_counit_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (I : C)
  [inst_1 : CategoryTheory.ChosenPullbacksAlong (CategoryTheory.CategoryStruct.id I)]
  [inst_2 : CategoryTheory.ExponentiableMorphism (CategoryTheory.CategoryStruct.id I)]
  {Z : CategoryTheory.Functor (CategoryTheory.Over I) (CategoryTheory.Over I)}
  (h : CategoryTheory.Functor.id (CategoryTheory.Over I) ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Functor.whiskerRight (CategoryTheory.ExponentiableMorphism.pushforwardId I).hom
        (CategoryTheory.ChosenPullbacksAlong.pullback (CategoryTheory.CategoryStruct.id I)))
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.ExponentiableMorphism.pullbackPushforwardAdj (CategoryTheory.CategoryStruct.id I)).counit h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ExponentiableMorphism.pullbackPushforwardAdj (CategoryTheory.CategoryStruct.id I)).counit h

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlongCategoryTheory.ExponentiableMorphism