Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.curry_uncurry

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {A X Y : C}
  [inst_2 : CategoryTheory.Closed A] (f : X ⟶ A ⟹ Y),
  CategoryTheory.MonoidalClosed.curry (CategoryTheory.MonoidalClosed.uncurry f) = f

Defined in: Mathlib.CategoryTheory.Monoidal.Closed.Basic
Cited by: 5 results in Mathlib
Foundations: Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.Closed

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Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.Adjunction.homEquivproof · cited by 202
CategoryTheory.ihomstatement and proof · cited by 179
CategoryTheory.Closedstatement and proof · cited by 90
Equiv.right_invproof · cited by 68
CategoryTheory.MonoidalClosed.uncurrystatement · cited by 46
CategoryTheory.MonoidalClosed.currystatement · cited by 44
CategoryTheory.Closed.adjproof · cited by 7

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.Over.sectionsCurry_sectionUncurryproof · cited by 2
CategoryTheory.MonoidalClosed.uncurry_pre_appproof · cited by 1
CategoryTheory.MonoidalClosed.uncurry_ihom_mapproof · cited by 1
CategoryTheory.MonoidalClosed.curry'_uncurry'proof · cited by 0
CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.left_triangle_componentsproof · cited by 0