Theorems · Theorem · category theory

CategoryTheory.Center.Hom.mk.inj

∀ {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

1 results in Mathlib

Foundations

Depth 15 from the axioms · uses no axioms