Theorems · Definition · category theory

CategoryTheory.ExponentiableMorphism.coev

{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] →
            CategoryTheory.Functor.id (CategoryTheory.Over J) ⟶
              (CategoryTheory.ChosenPullbacksAlong.pullback f).comp (CategoryTheory.ExponentiableMorphism.pushforward f)

The dependent coevaluation natural transformation as the unit of the adjunction.

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism

Cited by

7 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlongCategoryTheory.ExponentiableMorphism