Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.isBinaryBilimitOfIsLimit

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {X Y : C} → (t : CategoryTheory.Limits.BinaryBicone X Y) → CategoryTheory.Limits.IsLimit t.toCone → t.IsBilimit

In a preadditive category, any binary bicone which is a limit cone is in fact a bilimit bicone.

Defined in
Mathlib.CategoryTheory.Preadditive.Biproducts
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Preadditive
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Limits.preservesBinaryBiproduct_of_preservesBinaryProduct · cited by 2Limits.preservesBinaryBip…CategoryTheory.Limits.BinaryBicone.isBilimitOfKernelInl · cited by 0BinaryBicone.isBilimitOfK…CategoryTheory.Limits.BinaryBicone.isBilimitOfKernelInr · cited by 0BinaryBicone.isBilimitOfK…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.IsLimit · cited by 664Limits.IsLimitCategoryTheory.Limits.pair · cited by 536Limits.pairCategoryTheory.Limits.BinaryBicone · cited by 111Limits.BinaryBiconeCategoryTheory.Limits.BinaryBicone.IsBilimit · cited by 26BinaryBicone.IsBilimitCategoryTheory.Limits.BinaryBicone.toCone · cited by 18BinaryBicone.toConeCategoryTheory.Limits.isBinaryBilimitOfTotal · cited by 1Limits.isBinaryBilimitOfT…Limits.isBinaryBilimitOfIsLim…CITED BYCITES

Cites10

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

Cited by3

Results whose statement or proof uses this declaration.