Theorems · Definition · category theory

CategoryTheory.Functor.FullyFaithful.monObj

{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} →
              [F.OplaxMonoidal] →
                F.FullyFaithful → (X : C) → [CategoryTheory.MonObj (F.obj X)] → CategoryTheory.MonObj X

Pullback a monoid object along a fully faithful oplax monoidal functor.

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

3 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.OplaxMonoidalCategoryTheory.MonObj