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Theorems · Definition · category theory

CategoryTheory.Limits.BinaryBicone.toCone

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

Extract the cone from a binary bicone.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
18 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

CategoryTheory.Limits.biprod.map · cited by 27biprod.mapCategoryTheory.Limits.BinaryBiproduct.isLimit · cited by 14BinaryBiproduct.isLimitCategoryTheory.Limits.BinaryBicone.IsBilimit.isLimit · cited by 7IsBilimit.isLimitCategoryTheory.Limits.biprod.map_fst · cited by 6biprod.map_fstCategoryTheory.Limits.biprod.map_snd · cited by 5biprod.map_sndCategoryTheory.Limits.preservesBinaryBiproduct_of_preservesBinaryProduct · cited by 2Limits.preservesBinaryBip…CategoryTheory.Limits.pointwiseBinaryBicone.isBilimit · cited by 2pointwiseBinaryBicone.isB…CategoryTheory.Limits.biprod.map_eq_map' · cited by 2biprod.map_eq_map'CategoryTheory.Limits.BinaryBicone.IsBilimit.mk.inj · cited by 1mk.injCategoryTheory.Limits.BinaryBicone.IsBilimit.mk.noConfusion · cited by 1mk.noConfusionCategoryTheory.Limits.isBinaryBilimitOfIsLimit · cited by 1Limits.isBinaryBilimitOfI…CategoryTheory.Limits.isBinaryBilimitOfTotal · cited by 1Limits.isBinaryBilimitOfT…CategoryTheory.Limits.biprod.conePointUniqueUpToIso_hom · cited by 0biprod.conePointUniqueUpT…CategoryTheory.Limits.biprod.conePointUniqueUpToIso_inv · cited by 0biprod.conePointUniqueUpT…CategoryTheory.Limits.BinaryBicone.IsBilimit.mk.injEq · cited by 0mk.injEqCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.Cone · cited by 710Limits.ConeCategoryTheory.Limits.pair · cited by 536Limits.pairCategoryTheory.Limits.BinaryFan.mk · cited by 112BinaryFan.mkCategoryTheory.Limits.BinaryBicone · cited by 111Limits.BinaryBiconeCategoryTheory.Limits.BinaryBicone.snd · cited by 48BinaryBicone.sndCategoryTheory.Limits.BinaryBicone.fst · cited by 48BinaryBicone.fstBinaryBicone.toConeCITED BYCITES

Cites10

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Cited by36

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