Theorems · Theorem · category theory

CategoryTheory.leftAdjointMate_comp_evaluation_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {X Y : C}
  [inst_2 : CategoryTheory.HasLeftDual X] [inst_3 : CategoryTheory.HasLeftDual Y] (f : X ⟶ Y) {Z : C}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorUnit C ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X (ᘁf))
      (CategoryTheory.CategoryStruct.comp (ε_ (ᘁX) X) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f ᘁY)
      (CategoryTheory.CategoryStruct.comp (ε_ (ᘁY) Y) h)

Defined in

Mathlib.CategoryTheory.Monoidal.Rigid.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.HasLeftDualCategoryTheory.HasLeftDual