Theorems · Theorem · category theory

CategoryTheory.yonedaAddGrp_naturality_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {G H X Y : C} [inst_2 : CategoryTheory.AddGrpObj G] [inst_3 : CategoryTheory.AddGrpObj H]
  (α : CategoryTheory.yonedaAddGrpObj G ⟶ CategoryTheory.yonedaAddGrpObj H) (f : X ⟶ Y) (g : Y ⟶ G) {Z : C} (h : H ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.ConcreteCategory.hom (α.app (Opposite.op X))) (CategoryTheory.CategoryStruct.comp f g)) h =
    CategoryTheory.CategoryStruct.comp f
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.ConcreteCategory.hom (α.app (Opposite.op Y))) g) h)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Grp

Cited by

0 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.AddGrpObjCategoryTheory.AddGrpObj