Theorems · Definition · category theory

CategoryTheory.Mat_.embeddingLiftIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {D : Type u₁} →
        [inst_2 : CategoryTheory.Category.{v₁, u₁} D] →
          [inst_3 : CategoryTheory.Preadditive D] →
            [inst_4 : CategoryTheory.Limits.HasFiniteBiproducts D] →
              (F : CategoryTheory.Functor C D) →
                [inst_5 : F.Additive] → (CategoryTheory.Mat_.embedding C).comp (CategoryTheory.Mat_.lift F) ≅ F

An additive functor C ⥤ D factors through its lift to Mat_ C ⥤ D.

Defined in

Mathlib.CategoryTheory.Preadditive.Mat

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasFiniteBiproductsCategoryTheory.Functor.Additive