Theorems · Theorem · category theory

CategoryTheory.Center.Hom.mk.injEq

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  {X Y : CategoryTheory.Center C} (f : X.fst ⟶ Y.fst)
  (comm :
    autoParam
      (∀ (U : C),
        CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f U) (Y.snd.β U).hom =
          CategoryTheory.CategoryStruct.comp (X.snd.β U).hom (CategoryTheory.MonoidalCategoryStruct.whiskerLeft U f))
      CategoryTheory.Center.Hom.comm._autoParam)
  (f_1 : X.fst ⟶ Y.fst)
  (comm_1 :
    autoParam
      (∀ (U : C),
        CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f_1 U) (Y.snd.β U).hom =
          CategoryTheory.CategoryStruct.comp (X.snd.β U).hom (CategoryTheory.MonoidalCategoryStruct.whiskerLeft U f_1))
      CategoryTheory.Center.Hom.comm._autoParam),
  ({ f := f, comm := comm } = { f := f_1, comm := comm_1 }) = (f = f_1)

Defined in

Mathlib.CategoryTheory.Monoidal.Center

Cited by

0 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory