Theorems · Definition · category theory

CategoryTheory.Functor.flipIsoCurrySwapUncurry

{C : Type u₂} →
  [inst : CategoryTheory.Category.{v₂, u₂} C] →
    {D : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} D] →
        {E : Type u₄} →
          [inst_2 : CategoryTheory.Category.{v₄, u₄} E] →
            (F : CategoryTheory.Functor C (CategoryTheory.Functor D E)) →
              F.flip ≅
                CategoryTheory.Functor.curry.obj
                  ((CategoryTheory.Prod.swap D C).comp (CategoryTheory.Functor.uncurry.obj F))

F.flip is isomorphic to uncurrying F, swapping the variables, and currying.

Defined in

Mathlib.CategoryTheory.Functor.Currying

Cited by

6 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category