Theorems · Theorem · category theory

CategoryTheory.ExponentiableMorphism.unit_pushforwardId_hom

∀ {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)],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ExponentiableMorphism.pullbackPushforwardAdj (CategoryTheory.CategoryStruct.id I)).unit
      ((CategoryTheory.ChosenPullbacksAlong.pullback (CategoryTheory.CategoryStruct.id I)).whiskerLeft
        (CategoryTheory.ExponentiableMorphism.pushforwardId I).hom) =
    (CategoryTheory.ExponentiableMorphism.pullbackPushforwardAdj (CategoryTheory.CategoryStruct.id I)).unit

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism

Cited by

1 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlongCategoryTheory.ExponentiableMorphism