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Theorems · Definition · category theory

CategoryTheory.Limits.BinaryBiproduct.isLimit

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (P Q : C) →
        [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct P Q] →
          CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.BinaryBiproduct.bicone P Q).toCone

BinaryBiproduct.bicone P Q is a limit cone.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
14 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct
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CategoryTheory.Limits.biprod.lift · cited by 79biprod.liftCategoryTheory.Limits.biprod.hom_ext · cited by 34biprod.hom_extCategoryTheory.Limits.biprod.lift_snd · cited by 33biprod.lift_sndCategoryTheory.Limits.biprod.lift_fst · cited by 31biprod.lift_fstCategoryTheory.Limits.biprod.map · cited by 27biprod.mapAddCommGrpCat.biprodIsoProd · cited by 10AddCommGrpCat.biprodIsoPr…CategoryTheory.Limits.biprod.map_fst · cited by 6biprod.map_fstCategoryTheory.Limits.biprod.map_snd · cited by 5biprod.map_sndModuleCat.biprodIsoProd · cited by 4ModuleCat.biprodIsoProdCategoryTheory.Limits.biprod.isoProd · cited by 3biprod.isoProdCategoryTheory.Limits.biprod.isoProd_hom · cited by 3biprod.isoProd_homCategoryTheory.Limits.pointwiseBinaryBicone.isBilimit · cited by 2pointwiseBinaryBicone.isB…CategoryTheory.Limits.biprod.map_eq_map' · cited by 2biprod.map_eq_map'CategoryTheory.Limits.biprod.isKernelFstKernelFork · cited by 2biprod.isKernelFstKernelF…CategoryTheory.Limits.biprod.isKernelSndKernelFork · cited by 2biprod.isKernelSndKernelF…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.IsLimit · cited by 664Limits.IsLimitCategoryTheory.Limits.pair · cited by 536Limits.pairCategoryTheory.Limits.HasBinaryBiproduct · cited by 251Limits.HasBinaryBiproductCategoryTheory.Limits.BinaryBiproduct.bicone · cited by 68BinaryBiproduct.biconeCategoryTheory.Limits.BinaryBicone.toCone · cited by 18BinaryBicone.toConeCategoryTheory.Limits.BinaryBicone.IsBilimit.isLimit · cited by 7IsBilimit.isLimitCategoryTheory.Limits.getBinaryBiproductData · cited by 5Limits.getBinaryBiproduct…CategoryTheory.Limits.BinaryBiproductData.isBilimit · cited by 1BinaryBiproductData.isBil…BinaryBiproduct.isLimitCITED BYCITES

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