Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.coev_app_comp_pre_app_assoc

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

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ClosedCategoryTheory.Closed