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Theorems · Definition · category theory

CategoryTheory.Limits.BinaryBiproductData.bicone

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

A bicone over P Q : C, which is both a limit cone and a colimit cocone.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
13 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

CategoryTheory.Limits.BinaryBiproduct.bicone · cited by 68BinaryBiproduct.biconeCategoryTheory.Limits.BinaryBiproductData.op · cited by 5BinaryBiproductData.opCategoryTheory.Limits.biprod.opIso_hom_fst · cited by 3biprod.opIso_hom_fstCategoryTheory.Limits.biprod.opIso_hom_snd · cited by 3biprod.opIso_hom_sndCategoryTheory.Limits.BinaryBiproductData.ofIso · cited by 2BinaryBiproductData.ofIsoCategoryTheory.Pretriangulated.exists_iso_binaryBiproduct_of_distTriang · cited by 1Pretriangulated.exists_is…CategoryTheory.Limits.biprod.inl_opIso_inv · cited by 1biprod.inl_opIso_invCategoryTheory.Limits.BinaryBiproductData.isBilimit · cited by 1BinaryBiproductData.isBil…CategoryTheory.Limits.biprod.inr_opIso_inv · cited by 1biprod.inr_opIso_invCategoryTheory.Limits.pointwiseBinaryBiproductData_bicone · cited by 0Limits.pointwiseBinaryBip…CategoryTheory.Pretriangulated.binaryBiproductData_bicone_inl · cited by 0Pretriangulated.binaryBip…CategoryTheory.Limits.BinaryBiproductData.ofIso_bicone · cited by 0BinaryBiproductData.ofIso…CategoryTheory.Pretriangulated.binaryBiproductData_bicone_fst · cited by 0Pretriangulated.binaryBip…CategoryTheory.Limits.BinaryBiproductData.op_bicone · cited by 0BinaryBiproductData.op_bi…CategoryTheory.Pretriangulated.binaryBiproductData_bicone_inr · cited by 0Pretriangulated.binaryBip…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.BinaryBicone · cited by 111Limits.BinaryBiconeCategoryTheory.Limits.BinaryBiproductData · cited by 8Limits.BinaryBiproductDataBinaryBiproductData.biconeCITED BYCITES

Cites4

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Cited by17

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