Theorems · Definition · category theory

CategoryTheory.Limits.BinaryBiproduct.isColimit

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (P Q : C) →
        [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct P Q] →
          CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.BinaryBiproduct.bicone P Q).toCocone

BinaryBiproduct.bicone P Q is a colimit cocone.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 8 results in Mathlib
Foundations: Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproduct

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Dashed lines are statement dependencies; solid lines are citations in proofs.

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
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Discretestatement · cited by 2,447
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.IsColimitstatement · cited by 773
CategoryTheory.Limits.pairstatement · cited by 536
CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
CategoryTheory.Limits.BinaryBiproduct.biconestatement · cited by 68
CategoryTheory.Limits.BinaryBicone.toCoconestatement · cited by 16
CategoryTheory.Limits.BinaryBicone.IsBilimit.isColimitproof · cited by 5
CategoryTheory.Limits.getBinaryBiproductDataproof · cited by 5
CategoryTheory.Limits.BinaryBiproductData.isBilimitproof · cited by 1

Cited by15

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.biprod.descproof · cited by 54
CategoryTheory.Limits.biprod.hom_ext'proof · cited by 30
CategoryTheory.Limits.biprod.inl_descproof · cited by 20
CategoryTheory.Limits.biprod.inr_descproof · cited by 18
CategoryTheory.Limits.biprod.inl_mapproof · cited by 3
CategoryTheory.Limits.biprod.inr_mapproof · cited by 3
CategoryTheory.Limits.pointwiseBinaryBicone.isBilimitproof · cited by 2
CategoryTheory.Limits.biprod.map_eq_map'proof · cited by 2
CategoryTheory.Limits.biprod.isCokernelInlCokernelForkproof · cited by 2
CategoryTheory.Limits.biprod.isCokernelInrCokernelForkproof · cited by 2
CategoryTheory.Limits.biprod.isoCoprodproof · cited by 2
CategoryTheory.Limits.biprod.map'proof · cited by 1