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Theorems · Definition · category theory

CategoryTheory.Limits.BinaryBiproduct.bicone

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (P Q : C) → [CategoryTheory.Limits.HasBinaryBiproduct P Q] → CategoryTheory.Limits.BinaryBicone P Q

A bicone for P Q which is both a limit cone and a colimit cocone.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
68 results in Mathlib
Foundations
Depth 5 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct
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Around this declaration

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

CategoryTheory.Limits.biprod · cited by 312Limits.biprodCategoryTheory.Limits.biprod.snd · cited by 132biprod.sndCategoryTheory.Limits.biprod.inl · cited by 127biprod.inlCategoryTheory.Limits.biprod.fst · cited by 121biprod.fstCategoryTheory.Limits.biprod.inr · cited by 109biprod.inrCategoryTheory.Limits.biprod.map · cited by 27biprod.mapCategoryTheory.Limits.BinaryBiproduct.isLimit · cited by 14BinaryBiproduct.isLimitCategoryTheory.Limits.BinaryBiproduct.isBilimit · cited by 13BinaryBiproduct.isBilimitCategoryTheory.Limits.BinaryBiproduct.isColimit · cited by 8BinaryBiproduct.isColimitHomologicalComplex.homotopyCofiber.inrX_sndX · cited by 8homotopyCofiber.inrX_sndXCategoryTheory.Limits.biprod.lift_desc · cited by 7biprod.lift_descHomologicalComplex.homotopyCofiber.inrX_fstX · cited by 7homotopyCofiber.inrX_fstXCategoryTheory.Limits.biprod.map_fst · cited by 6biprod.map_fstHomologicalComplex.homotopyCofiber.inlX_fstX · cited by 6homotopyCofiber.inlX_fstXHomologicalComplex.homotopyCofiber.inlX_sndX · cited by 6homotopyCofiber.inlX_sndXCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct · cited by 251Limits.HasBinaryBiproductCategoryTheory.Limits.BinaryBicone · cited by 111Limits.BinaryBiconeCategoryTheory.Limits.BinaryBiproductData.bicone · cited by 13BinaryBiproductData.biconeCategoryTheory.Limits.getBinaryBiproductData · cited by 5Limits.getBinaryBiproduct…BinaryBiproduct.biconeCITED BYCITES

Cites6

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Cited by83

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