Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.BinaryBiproduct.isBilimit

{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.BinaryBiproduct.bicone P Q).IsBilimit

BinaryBiproduct.bicone P Q is a limit bicone.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
13 results in Mathlib
Foundations
Depth 6 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Functor.mapBiprod · cited by 13Functor.mapBiprodHomologicalComplex.homotopyCofiber.inlX_mapHomologicalComplexObjXIso_inv · cited by 1homotopyCofiber.inlX_mapH…HomologicalComplex.homotopyCofiber.inrX_mapHomologicalComplexObjXIso_inv · cited by 1homotopyCofiber.inrX_mapH…CategoryTheory.Abelian.Ext.biprod_ext · cited by 1Ext.biprod_extCategoryTheory.IsPullback.inl_snd · cited by 0IsPullback.inl_sndCategoryTheory.IsPullback.inr_fst · cited by 0IsPullback.inr_fstCategoryTheory.IsPushout.inl_snd · cited by 0IsPushout.inl_sndCategoryTheory.IsPushout.inr_fst · cited by 0IsPushout.inr_fstCategoryTheory.IsPushout.of_hasBinaryBiproduct · cited by 0IsPushout.of_hasBinaryBip…CategoryTheory.IsPushout.of_has_biproduct · cited by 0IsPushout.of_has_biproductCategoryTheory.IsPullback.of_hasBinaryBiproduct · cited by 0IsPullback.of_hasBinaryBi…CategoryTheory.BicartesianSq.of_has_biproduct₁ · cited by 0BicartesianSq.of_has_bipr…CategoryTheory.BicartesianSq.of_has_biproduct₂ · cited by 0BicartesianSq.of_has_bipr…CategoryTheory.IsPullback.of_has_biproduct · cited by 0IsPullback.of_has_biprodu…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct · cited by 251Limits.HasBinaryBiproductCategoryTheory.Limits.BinaryBiproduct.bicone · cited by 68BinaryBiproduct.biconeCategoryTheory.Limits.BinaryBicone.IsBilimit · cited by 26BinaryBicone.IsBilimitCategoryTheory.Limits.getBinaryBiproductData · cited by 5Limits.getBinaryBiproduct…CategoryTheory.Limits.BinaryBiproductData.isBilimit · cited by 1BinaryBiproductData.isBil…BinaryBiproduct.isBilimitCITED BYCITES

Cites7

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

Cited by14

Results whose statement or proof uses this declaration.