Theorems · Theorem · category theory

CategoryTheory.Over.sectionsUncurry_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)]
  [inst_4 : CategoryTheory.BraidedCategory C] {X : CategoryTheory.Over I} {A : C}
  {u : (CategoryTheory.toOver I).obj A ⟶ X},
  CategoryTheory.Over.sectionsUncurry (CategoryTheory.Over.sectionsCurry u) = u

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.Sections

Cited by

2 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.ClosedCategoryTheory.ChosenPullbacksAlongCategoryTheory.BraidedCategory