Theorems · Theorem · category theory

CategoryTheory.Functor.FullyFaithful.addMonObj_add

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {D : Type u₂}
  [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.MonoidalCategory D]
  {F : CategoryTheory.Functor C D} [inst_4 : F.OplaxMonoidal] (hF : F.FullyFaithful) (X : C)
  [inst_5 : CategoryTheory.AddMonObj (F.obj X)],
  CategoryTheory.AddMonObj.add =
    hF.preimage
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OplaxMonoidal.δ F X X) CategoryTheory.AddMonObj.add)

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

0 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.OplaxMonoidalCategoryTheory.AddMonObj