Theorems · Definition · category theory

CategoryTheory.Limits.isBilimitBinaryBiconeOfIsSplitMonoOfCokernel

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {X Y : C} →
        {f : X ⟶ Y} →
          [inst_2 : CategoryTheory.IsSplitMono f] →
            {c : CategoryTheory.Limits.CokernelCofork f} →
              (i : CategoryTheory.Limits.IsColimit c) →
                (CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel i).IsBilimit

The bicone constructed in binaryBiconeOfSplitMonoOfCokernel is a bilimit. This is a version of the splitting lemma that holds in all preadditive categories.

Defined in

Mathlib.CategoryTheory.Preadditive.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.IsSplitMono