Theorems · Theorem · category theory

CategoryTheory.AddGrpObj.sub_comp_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {G H X : C} [inst_2 : CategoryTheory.AddGrpObj G] [inst_3 : CategoryTheory.AddGrpObj H] (f g : X ⟶ G) (h : G ⟶ H)
  [CategoryTheory.IsAddMonHom h] {Z : C} (h_1 : H ⟶ Z),
  CategoryTheory.CategoryStruct.comp (f - g) (CategoryTheory.CategoryStruct.comp h h_1) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f h - CategoryTheory.CategoryStruct.comp g h)
      h_1

Defined in: Mathlib.CategoryTheory.Monoidal.Cartesian.Grp
Cited by: 0 results in Mathlib
Foundations: Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory CategoryTheory.AddGrpObj CategoryTheory.AddGrpObj CategoryTheory.IsAddMonHom

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
CategoryTheory.AddGrpObjstatement and proof · cited by 88
CategoryTheory.IsAddMonHomstatement and proof · cited by 49
CategoryTheory.Hom.addGroupstatement · cited by 25
CategoryTheory.AddGrpObj.sub_compproof · cited by 1

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