Theorems · Definition · category theory

CategoryTheory.ExponentiableMorphism.pushforwardUncurry

{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] →
            {X : CategoryTheory.Over I} →
              {A : CategoryTheory.Over J} →
                (A ⟶ (CategoryTheory.ExponentiableMorphism.pushforward f).obj X) →
                  ((CategoryTheory.ChosenPullbacksAlong.pullback f).obj A ⟶ X)

The uncurrying of A ⟶ (pushforward f).obj X in Over J to a morphism (Over.pullback f).obj A ⟶ X in Over I.

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlongCategoryTheory.ExponentiableMorphism