Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.uncurry_ihomCurry

∀ {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)],
  CategoryTheory.MonoidalClosed.uncurry (CategoryTheory.MonoidalClosed.ihomCurry x y z) =
    CategoryTheory.MonoidalClosed.curry
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.associator x y
            (CategoryTheory.MonoidalCategoryStruct.tensorObj x y ⟹ z)).inv
        ((CategoryTheory.ihom.ev (CategoryTheory.MonoidalCategoryStruct.tensorObj x y)).app z))

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.InternalCurrying

Cited by

1 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ClosedCategoryTheory.ClosedCategoryTheory.Closed