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Theorems · Definition · category theory

CategoryTheory.Limits.binaryBiconeIsBilimitOfLimitConeOfIsLimit

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

We can turn any limit cone over a pair into a bilimit bicone.

Defined in
Mathlib.CategoryTheory.Preadditive.Biproducts
Cited by
2 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Preadditive
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CategoryTheory.Limits.HasBinaryBiproduct.of_hasBinaryProduct · cited by 1HasBinaryBiproduct.of_has…CategoryTheory.Limits.preservesBinaryProduct_of_preservesBinaryBiproduct · cited by 0Limits.preservesBinaryPro…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.Cone · cited by 710Limits.ConeCategoryTheory.Limits.IsLimit · cited by 664Limits.IsLimitCategoryTheory.Limits.pair · cited by 536Limits.pairCategoryTheory.Limits.BinaryBicone.IsBilimit · cited by 26BinaryBicone.IsBilimitCategoryTheory.Limits.BinaryBicone.ofLimitCone · cited by 7BinaryBicone.ofLimitConeCategoryTheory.Limits.isBinaryBilimitOfTotal · cited by 1Limits.isBinaryBilimitOfT…Limits.binaryBiconeIsBilimitO…CITED BYCITES

Cites10

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Cited by2

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