Theorems · Definition · category theory

CategoryTheory.Free.ext

(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] →
              [inst_4 : CategoryTheory.Linear R D] →
                {F G : CategoryTheory.Functor (CategoryTheory.Free R C) D} →
                  [F.Additive] →
                    [CategoryTheory.Functor.Linear R F] →
                      [G.Additive] →
                        [CategoryTheory.Functor.Linear R G] →
                          ((CategoryTheory.Free.embedding R C).comp F ≅ (CategoryTheory.Free.embedding R C).comp G) →
                            (F ≅ G)

Two R-linear functors out of the R-linear completion are isomorphic iff their compositions with the embedding functor are isomorphic.

Defined in

Mathlib.Algebra.Category.ModuleCat.Adjunctions

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.LinearCategoryTheory.Functor.AdditiveCategoryTheory.Functor.LinearCategoryTheory.Functor.AdditiveCategoryTheory.Functor.Linear