Theorems · Theorem · category theory

CategoryTheory.unitOfTensorIsoUnit_inv_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {M : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} M]
  [inst_2 : CategoryTheory.MonoidalCategory M] (F : CategoryTheory.Functor M (CategoryTheory.Functor C C)) (m n : M)
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj m n ≅ CategoryTheory.MonoidalCategoryStruct.tensorUnit M)
  [inst_3 : F.Monoidal] (X : C),
  (CategoryTheory.unitOfTensorIsoUnit F m n h).inv.app X =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.LaxMonoidal.ε F).app X)
      (CategoryTheory.CategoryStruct.comp ((F.map h.inv).app X) ((CategoryTheory.Functor.OplaxMonoidal.δ F m n).app X))

Defined in

Mathlib.CategoryTheory.Monoidal.End

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.Monoidal