Theorems · Theorem · category theory

CategoryTheory.AddGrpObj.sub_comp

∀ {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],
  CategoryTheory.CategoryStruct.comp (f - g) h =
    CategoryTheory.CategoryStruct.comp f h - CategoryTheory.CategoryStruct.comp g h

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Grp

Cited by

1 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.AddGrpObjCategoryTheory.AddGrpObjCategoryTheory.IsAddMonHom