Theorems · Inductive type · category theory

CategoryTheory.Functor.Linear

(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] →
                [CategoryTheory.Linear R C] → [CategoryTheory.Linear R D] → CategoryTheory.Functor C D → Prop

An additive functor F is R-linear provided F.map is an R-module morphism.

Defined in

Mathlib.CategoryTheory.Linear.LinearFunctor

Cited by

25 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

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