Theorems · Theorem · category theory

CategoryTheory.frobeniusMorphism_mate

∀ {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) {L : CategoryTheory.Functor D C} [inst_4 : CategoryTheory.MonoidalClosed C]
  [inst_5 : CategoryTheory.MonoidalClosed D]
  [inst_6 : CategoryTheory.Limits.PreservesLimitsOfShape (CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair) F]
  (h : L ⊣ F) (A : C),
  (CategoryTheory.conjugateEquiv (h.comp (CategoryTheory.ihom.adjunction A))
        ((CategoryTheory.ihom.adjunction (F.obj A)).comp h))
      (CategoryTheory.frobeniusMorphism F h A).natTrans =
    (CategoryTheory.expComparison F A).natTrans

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Functor

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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