Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.curry_pre_app

∀ {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 Y : C}
  (g : CategoryTheory.MonoidalCategoryStruct.tensorObj A Y ⟶ X),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalClosed.curry g)
      ((CategoryTheory.MonoidalClosed.pre f).app X) =
    CategoryTheory.MonoidalClosed.curry
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Y) g)

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Basic

Cited by

2 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ClosedCategoryTheory.Closed