Theorems · Theorem · category theory

CategoryTheory.Preadditive.comp_add

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.Preadditive C] (P Q R : C) (f : P ⟶ Q)
  (g g' : Q ⟶ R),
  CategoryTheory.CategoryStruct.comp f (g + g') =
    CategoryTheory.CategoryStruct.comp f g + CategoryTheory.CategoryStruct.comp f g'

A category is called preadditive if P ⟶ Q is an abelian group such that composition is linear in both variables.

Defined in

Mathlib.CategoryTheory.Preadditive.Basic

Cited by

65 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.Preadditive