Theorems · Theorem · category theory

CategoryTheory.Functor.FullyFaithful.grpObj_one

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {D : Type u₂} [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.CartesianMonoidalCategory D]
  {F : CategoryTheory.Functor C D} [inst_4 : F.Monoidal] (hF : F.FullyFaithful) (X : C)
  [inst_5 : CategoryTheory.GrpObj (F.obj X)],
  CategoryTheory.MonObj.one =
    hF.preimage
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OplaxMonoidal.η F) CategoryTheory.MonObj.one)

Defined in

Mathlib.CategoryTheory.Monoidal.Grp

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.Functor.MonoidalCategoryTheory.GrpObj