Theorems · Theorem · category theory

CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom_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.ChosenPullbacksAlong.pullback (CategoryTheory.CategoryStruct.id I)).comp
        (CategoryTheory.Functor.id (CategoryTheory.Over I)) ⟶
      Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ExponentiableMorphism.pullbackPushforwardAdj (CategoryTheory.CategoryStruct.id I)).unit
      (CategoryTheory.CategoryStruct.comp
        ((CategoryTheory.ChosenPullbacksAlong.pullback (CategoryTheory.CategoryStruct.id I)).whiskerLeft
          (CategoryTheory.ExponentiableMorphism.pushforwardId I).hom)
        h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ExponentiableMorphism.pullbackPushforwardAdj (CategoryTheory.CategoryStruct.id I)).unit 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