Theorems · Definition · category theory

CategoryTheory.MonoidalClosed.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)] →
              y ⟹ x ⟹ z ⟶ CategoryTheory.MonoidalCategoryStruct.tensorObj x y ⟹ z

The uncurrying operation taking a morphism y ⟶ C(x, z) to a morphism (x ⊗ y) ⟶ z, constructed as a morphism in C between internal homs.

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.InternalCurrying

Cited by

6 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ClosedCategoryTheory.ClosedCategoryTheory.Closed