Theorems · Theorem · category theory

CategoryTheory.Functor.comp_mapGrp_one_assoc

∀ {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]
  (A : CategoryTheory.Grp C) {Z : E} (h : ((F.comp G).mapGrp.obj A).X ⟶ Z),
  CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.one h =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.ε (F.comp G))
        (G.map (F.map CategoryTheory.MonObj.one)))
      h

Defined in

Mathlib.CategoryTheory.Monoidal.Grp

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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