Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.uncurry_ihomUncurry

∀ {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.ihomUncurry x y z) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator x y (y ⟹ x ⟹ z)).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerLeft x ((CategoryTheory.ihom.ev y).app (x ⟹ z)))
        ((CategoryTheory.ihom.ev x).app z))

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.InternalCurrying

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ClosedCategoryTheory.ClosedCategoryTheory.Closed