Theorems · Theorem · category theory

CategoryTheory.ihom.ev_naturality_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (A : C)
  [inst_2 : CategoryTheory.Closed A] {X Y : C} (f : X ⟶ Y) {Z : C} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft A ((CategoryTheory.ihom A).map f))
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.ihom.ev A).app Y) h) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.ihom.ev A).app X) (CategoryTheory.CategoryStruct.comp f h)

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Closed