Theorems · Definition · category theory

CategoryTheory.Functor.mapAddGrpCompIso

{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] →
            {E : Type u₃} →
              [inst_4 : CategoryTheory.Category.{v₃, u₃} E] →
                [inst_5 : CategoryTheory.CartesianMonoidalCategory E] →
                  {F : CategoryTheory.Functor C D} →
                    {G : CategoryTheory.Functor D E} →
                      [inst_6 : F.Monoidal] →
                        [inst_7 : G.Monoidal] → (F.comp G).mapAddGrp ≅ F.mapAddGrp.comp G.mapAddGrp

The composition functor is also the composition on additive group objects.

Defined in

Mathlib.CategoryTheory.Monoidal.Grp

Cited by

6 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.Functor.MonoidalCategoryTheory.Functor.Monoidal