Theorems · Definition · category theory

CategoryTheory.Free.lift

(R : Type u_1) →
  [inst : CommRing R] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        {D : Type u} →
          [inst_2 : CategoryTheory.Category.{v, u} D] →
            [inst_3 : CategoryTheory.Preadditive D] →
              [CategoryTheory.Linear R D] →
                CategoryTheory.Functor C D → CategoryTheory.Functor (CategoryTheory.Free R C) D

A functor to an R-linear category lifts to a functor from its R-linear completion.

Defined in

Mathlib.Algebra.Category.ModuleCat.Adjunctions

Cited by

3 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Linear