Theorems · Definition · category theory

CategoryTheory.Limits.biprod.isCokernelInlCokernelFork

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (X Y : C) →
        [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y] →
          CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.biprod.inlCokernelCofork X Y)

The cofork biprod.inlCokernelFork is indeed a colimit.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 2 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproduct

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.IsColimitstatement · cited by 773
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.Limits.biprodstatement · cited by 312
CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
CategoryTheory.Limits.biprod.inlstatement · cited by 127
CategoryTheory.Limits.BinaryBiproduct.isColimitproof · cited by 8
CategoryTheory.Limits.biprod.inlCokernelCoforkstatement · cited by 3
CategoryTheory.Limits.BinaryBicone.isColimitInlCokernelCoforkproof · cited by 0

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.cokernelBiprodInlIsoproof · cited by 2
CategoryTheory.Limits.cokernelBiprodInlIso_homstatement · cited by 0
CategoryTheory.Limits.cokernelBiprodInlIso_invstatement · cited by 0