Theorems · Definition · category theory

CategoryTheory.Free.embeddingLiftIso

(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 : CategoryTheory.Functor C D) →
                  (CategoryTheory.Free.embedding R C).comp (CategoryTheory.Free.lift R F) ≅ F

The embedding into the R-linear completion, followed by the lift, is isomorphic to the original functor.

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.Linear