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Theorems · Definition · category theory

CategoryTheory.MonoidalClosed.curry

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      {A X Y : C} →
        [inst_2 : CategoryTheory.Closed A] → (CategoryTheory.MonoidalCategoryStruct.tensorObj A Y ⟶ X) → (Y ⟶ A ⟹ X)

Currying in a monoidal closed category.

Defined in
Mathlib.CategoryTheory.Monoidal.Closed.Basic
Cited by
44 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Closed

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.MonoidalClosed.uncurry_curry · cited by 15MonoidalClosed.uncurry_cu…CategoryTheory.MonoidalClosed.curry' · cited by 14MonoidalClosed.curry'CategoryTheory.MonoidalClosed.comp · cited by 13MonoidalClosed.compCategoryTheory.curryRightUnitorHom · cited by 8CategoryTheory.curryRight…CategoryTheory.MonoidalClosed.id · cited by 7MonoidalClosed.idCategoryTheory.MonoidalClosed.ihomCurry · cited by 7MonoidalClosed.ihomCurryCategoryTheory.MonoidalClosed.curry_natural_left · cited by 6MonoidalClosed.curry_natu…CategoryTheory.MonoidalClosed.ihomUncurry · cited by 6MonoidalClosed.ihomUncurryCategoryTheory.MonoidalClosed.curry_uncurry · cited by 5MonoidalClosed.curry_uncu…CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app · cited by 5DayConvolutionInternalHom…CategoryTheory.MonoidalClosed.comp_eq · cited by 4MonoidalClosed.comp_eqCategoryTheory.Over.sectionsCurry · cited by 4Over.sectionsCurryCategoryTheory.MonoidalClosed.curry_natural_right · cited by 4MonoidalClosed.curry_natu…CategoryTheory.MonoidalClosed.curry_injective · cited by 3MonoidalClosed.curry_inje…CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app_π · cited by 3DayConvolutionInternalHom…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.Adjunction.homEquiv · cited by 202Adjunction.homEquivCategoryTheory.ihom · cited by 179CategoryTheory.ihomCategoryTheory.Closed · cited by 90CategoryTheory.ClosedCategoryTheory.ihom.adjunction · cited by 31ihom.adjunctionMonoidalClosed.curryCITED BYCITES

Cites10

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Cited by56

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