Theorems · Theorem · category theory

CategoryTheory.AddMonObj.add_comp

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {M N X : C} [inst_2 : CategoryTheory.AddMonObj M] [inst_3 : CategoryTheory.AddMonObj N] (f₁ f₂ : X ⟶ M) (g : M ⟶ N)
  [CategoryTheory.IsAddMonHom g],
  CategoryTheory.CategoryStruct.comp (f₁ + f₂) g =
    CategoryTheory.CategoryStruct.comp f₁ g + CategoryTheory.CategoryStruct.comp f₂ g

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

3 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.AddMonObjCategoryTheory.AddMonObjCategoryTheory.IsAddMonHom