Theorems · Definition · category theory

CategoryTheory.Functor.grpObjObj

{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} →
              [F.Monoidal] → {G : C} → [CategoryTheory.GrpObj G] → CategoryTheory.GrpObj (F.obj G)

The image of a group object under a monoidal functor is a group object.

Defined in

Mathlib.CategoryTheory.Monoidal.Grp

Cited by

5 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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