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Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.lift_snd

∀ {C : Type uC} [inst : CategoryTheory.Category.{uC', uC} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {W X Y : C} [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y] (f : W ⟶ X) (g : W ⟶ Y),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.lift f g) CategoryTheory.Limits.biprod.snd = g
Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
33 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct
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CategoryTheory.Limits.biprod.lift_snd_assoc · cited by 4biprod.lift_snd_assocCategoryTheory.Abelian.Ext.add_hom · cited by 4Ext.add_homCategoryTheory.Functor.biprodComparison_snd · cited by 3Functor.biprodComparison_…CategoryTheory.Limits.biprod.opIso_hom_snd · cited by 3biprod.opIso_hom_sndHomologicalComplex.cylinder.map_ι₀_mapHomologicalComplexObjIso_hom · cited by 2cylinder.map_ι₀_mapHomolo…HomologicalComplex.cylinder.map_ι₁_mapHomologicalComplexObjIso_hom · cited by 2cylinder.map_ι₁_mapHomolo…CategoryTheory.Abelian.SpectralObject.kernelSequenceE_exact · cited by 2SpectralObject.kernelSequ…CochainComplex.cm5b.fac · cited by 2cm5b.facCategoryTheory.Limits.biprod.isoProd_inv · cited by 2biprod.isoProd_invCategoryTheory.kernelCokernelCompSequence.φ_snd · cited by 2kernelCokernelCompSequenc…CategoryTheory.Limits.biprod.symmetry' · cited by 2biprod.symmetry'CategoryTheory.Limits.biprod.braiding_map_braiding · cited by 1biprod.braiding_map_braid…CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply · cited by 1MayerVietorisSquare.toBip…HomologicalComplex.biprodXIso_hom_snd · cited by 1HomologicalComplex.biprod…HomologicalComplex.cylinder.πCompι₀Homotopy.inlX_nullHomotopy_f · cited by 1πCompι₀Homotopy.inlX_null…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.biprod · cited by 312Limits.biprodCategoryTheory.Limits.HasBinaryBiproduct · cited by 251Limits.HasBinaryBiproductCategoryTheory.Limits.biprod.snd · cited by 132biprod.sndCategoryTheory.Limits.BinaryFan.mk · cited by 112BinaryFan.mkCategoryTheory.Limits.biprod.lift · cited by 79biprod.liftCategoryTheory.Limits.IsLimit.fac · cited by 67IsLimit.facCategoryTheory.Limits.BinaryBiproduct.isLimit · cited by 14BinaryBiproduct.isLimitbiprod.lift_sndCITED BYCITES

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Cited by33

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