Theorems · Definition · category theory

CategoryTheory.ExponentiableMorphism.comp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {I J K : C} →
      (f : I ⟶ J) →
        (g : J ⟶ K) →
          [inst_1 : CategoryTheory.ChosenPullbacksAlong f] →
            [inst_2 : CategoryTheory.ChosenPullbacksAlong g] →
              [inst_3 : CategoryTheory.ChosenPullbacksAlong (CategoryTheory.CategoryStruct.comp f g)] →
                [CategoryTheory.ExponentiableMorphism f] →
                  [CategoryTheory.ExponentiableMorphism g] →
                    CategoryTheory.ExponentiableMorphism (CategoryTheory.CategoryStruct.comp f g)

The composition of exponentiable morphisms is exponentiable.

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism

Cited by

5 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlongCategoryTheory.ChosenPullbacksAlongCategoryTheory.ChosenPullbacksAlongCategoryTheory.ExponentiableMorphismCategoryTheory.ExponentiableMorphism