Theorems · Inductive type · category theory

CategoryTheory.Limits.BinaryBicone.IsBilimit

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

Structure witnessing that a binary bicone is a limit cone and a limit cocone.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 26 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms

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

Cites3

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

CategoryTheory.Categorystatement · cited by 32,673
CategoryTheory.Limits.HasZeroMorphismsstatement · cited by 3,275
CategoryTheory.Limits.BinaryBiconestatement · cited by 111

Cited by61

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.BinaryBiproduct.isBilimitstatement · cited by 13
CategoryTheory.Limits.BinaryBicone.IsBilimit.isLimitstatement and proof · cited by 7
CategoryTheory.Limits.isBinaryBilimitOfPreservesstatement and proof · cited by 6
CategoryTheory.Limits.BinaryBicone.IsBilimit.isColimitstatement and proof · cited by 5
CategoryTheory.IsPullback.of_isBilimitstatement and proof · cited by 4
CategoryTheory.IsPushout.of_isBilimitstatement and proof · cited by 4
CategoryTheory.Limits.biprod.uniqueUpToIsostatement and proof · cited by 3
CategoryTheory.IsPullback.inl_snd'statement and proof · cited by 2
CategoryTheory.IsPullback.of_is_bilimit'statement and proof · cited by 2
CategoryTheory.Limits.biprod.uniqueUpToIso_invstatement and proof · cited by 2
CategoryTheory.IsPushout.inl_snd'statement and proof · cited by 2
CategoryTheory.IsPushout.of_is_bilimit'statement and proof · cited by 2