Theorems · Theorem · category theory

CategoryTheory.Functor.map_smul

∀ {R : Type u_1} [inst : Semiring R] {C : Type u_2} {D : Type u_3} [inst_1 : CategoryTheory.Category.{v_1, u_2} C]
  [inst_2 : CategoryTheory.Category.{v_2, u_3} D] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : CategoryTheory.Preadditive D] [inst_5 : CategoryTheory.Linear R C] [inst_6 : CategoryTheory.Linear R D]
  (F : CategoryTheory.Functor C D) [CategoryTheory.Functor.Linear R F] {X Y : C} (r : R) (f : X ⟶ Y),
  F.map (r • f) = r • F.map f

Defined in

Mathlib.CategoryTheory.Linear.LinearFunctor

Cited by

10 results in Mathlib

Foundations

Depth 9 from the axioms · uses no axioms

Assumes

SemiringCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.PreadditiveCategoryTheory.LinearCategoryTheory.LinearCategoryTheory.Functor.Linear