Theorems · Theorem · category theory

CategoryTheory.Linear.comp_smul

∀ {R : Type w} {inst : Semiring R} {C : Type u} {inst_1 : CategoryTheory.Category.{v, u} C}
  {inst_2 : CategoryTheory.Preadditive C} [self : CategoryTheory.Linear R C] (X Y Z : C) (f : X ⟶ Y) (r : R)
  (g : Y ⟶ Z), CategoryTheory.CategoryStruct.comp f (r • g) = r • CategoryTheory.CategoryStruct.comp f g

compatibility of the scalar multiplication with the pre-composition

Defined in

Mathlib.CategoryTheory.Linear.Basic

Cited by

11 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

CategoryTheory.Linear