Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.id_tensor_pre_app_comp_ev

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] {A B : C}
  [inst_2 : CategoryTheory.Closed A] [inst_3 : CategoryTheory.Closed B] (f : B ⟶ A) (X : C),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft B ((CategoryTheory.MonoidalClosed.pre f).app X))
      ((CategoryTheory.ihom.ev B).app X) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f (A ⟹ X))
      ((CategoryTheory.ihom.ev A).app X)

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Basic

Cited by

3 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ClosedCategoryTheory.Closed