Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.ihomUncurry_ihomCurry_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (x y z : C)
  [inst_2 : CategoryTheory.Closed x] [inst_3 : CategoryTheory.Closed y]
  [inst_4 : CategoryTheory.Closed (CategoryTheory.MonoidalCategoryStruct.tensorObj x y)] {Z : C} (h : y ⟹ x ⟹ z ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalClosed.ihomUncurry x y z)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalClosed.ihomCurry x y z) h) =
    h

Defined in: Mathlib.CategoryTheory.Monoidal.Closed.InternalCurrying
Cited by: 0 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.Closed CategoryTheory.Closed CategoryTheory.Closed

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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.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.Category.id_compproof · cited by 1,998
CategoryTheory.ihomstatement and proof · cited by 179
CategoryTheory.Closedstatement and proof · cited by 90
CategoryTheory.MonoidalClosed.ihomCurrystatement and proof · cited by 7
CategoryTheory.MonoidalClosed.ihomUncurrystatement and proof · cited by 6

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