Theorems · Definition · category theory

CategoryTheory.expComparison

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u'} →
      [inst_1 : CategoryTheory.Category.{v, u'} D] →
        [inst_2 : CategoryTheory.CartesianMonoidalCategory C] →
          [inst_3 : CategoryTheory.CartesianMonoidalCategory D] →
            (F : CategoryTheory.Functor C D) →
              [inst_4 : CategoryTheory.MonoidalClosed C] →
                [inst_5 : CategoryTheory.MonoidalClosed D] →
                  [CategoryTheory.Limits.PreservesLimitsOfShape
                        (CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair) F] →
                    (A : C) → CategoryTheory.TwoSquare (CategoryTheory.ihom A) F F (CategoryTheory.ihom (F.obj A))

The exponential comparison map. F is a Cartesian closed functor if this is an iso for all A.

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Functor

Cited by

7 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.MonoidalClosedCategoryTheory.Limits.PreservesLimitsOfShape