Theorems · Definition · category theory

CategoryTheory.Limits.isBilimitBinaryBiconeOfIsSplitEpiOfKernel

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {X Y : C} →
        {f : X ⟶ Y} →
          [inst_2 : CategoryTheory.IsSplitEpi f] →
            {c : CategoryTheory.Limits.KernelFork f} →
              (i : CategoryTheory.Limits.IsLimit c) →
                (CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel i).IsBilimit

The bicone constructed in binaryBiconeOfIsSplitEpiOfKernel 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 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.IsSplitEpi

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.Iso.reflproof · cited by 727
CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
CategoryTheory.Limits.KernelForkstatement and proof · cited by 108
CategoryTheory.IsSplitEpistatement and proof · cited by 46
CategoryTheory.Limits.IsLimit.ofIsoLimitproof · cited by 39
CategoryTheory.Limits.BinaryBicone.IsBilimitstatement · cited by 26

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