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Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.uncurry_eq

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {A X Y : C}
  [inst_2 : CategoryTheory.Closed A] (g : Y ⟶ A ⟹ X),
  CategoryTheory.MonoidalClosed.uncurry g =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft A g)
      ((CategoryTheory.ihom.ev A).app X)
Defined in
Mathlib.CategoryTheory.Monoidal.Closed.Basic
Cited by
9 results in Mathlib
Foundations
Depth 26 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_id_eq_ev · cited by 6MonoidalClosed.uncurry_id…CategoryTheory.MonoidalClosed.curry_pre_app · cited by 2MonoidalClosed.curry_pre_…CategoryTheory.MonoidalClosed.id_comp · cited by 1MonoidalClosed.id_compCategoryTheory.MonoidalClosed.ihomCurry_ihomUncurry · cited by 1MonoidalClosed.ihomCurry_…CategoryTheory.MonoidalClosed.ihomUncurry_ihomCurry · cited by 1MonoidalClosed.ihomUncurr…CategoryTheory.MonoidalClosed.assoc · cited by 1MonoidalClosed.assocCategoryTheory.MonoidalClosed.uncurry_pre · cited by 1MonoidalClosed.uncurry_preCategoryTheory.uncurry_expComparison · cited by 0CategoryTheory.uncurry_ex…CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_naturality_app · cited by 0DayConvolutionInternalHom…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.whiskerLeft · cited by 915MonoidalCategoryStruct.wh…CategoryTheory.ihom · cited by 179CategoryTheory.ihomCategoryTheory.MonoidalCategory.tensorLeft · cited by 170MonoidalCategory.tensorLe…CategoryTheory.Closed · cited by 90CategoryTheory.ClosedCategoryTheory.MonoidalClosed.uncurry · cited by 46MonoidalClosed.uncurryCategoryTheory.ihom.ev · cited by 38ihom.evMonoidalClosed.uncurry_eqCITED BYCITES

Cites15

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Cited by9

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