Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.compTranspose_eq

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (x y z : C)
  [inst_2 : CategoryTheory.Closed x] [inst_3 : CategoryTheory.Closed y],
  CategoryTheory.MonoidalClosed.compTranspose x y z =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator x (x ⟹ y) (y ⟹ z)).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight ((CategoryTheory.ihom.ev x).app y) (y ⟹ z))
        ((CategoryTheory.ihom.ev y).app z))

Unfold the definition of compTranspose. This exists to streamline the proof of MonoidalClosed.assoc

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.Basic

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.ClosedCategoryTheory.Closed