Theorems · Definition · category theory

CategoryTheory.Over.sectionsCurry

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      {I : C} →
        [inst_2 : CategoryTheory.Closed I] →
          [inst_3 : CategoryTheory.ChosenPullbacksAlong (CategoryTheory.curryRightUnitorHom I)] →
            [CategoryTheory.BraidedCategory C] →
              {X : CategoryTheory.Over I} →
                {A : C} → ((CategoryTheory.toOver I).obj A ⟶ X) → (A ⟶ (CategoryTheory.Over.sections I).obj X)

The currying operation Hom ((toOver I).obj A) X → Hom A (I ⟹ X.left).

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.Sections

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.ClosedCategoryTheory.ChosenPullbacksAlongCategoryTheory.BraidedCategory