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Theorems · Definition · category theory

CategoryTheory.Limits.biprod.snd

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {X Y : C} → [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y] → X ⊞ Y ⟶ Y

The projection onto the second summand of a binary biproduct.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
132 results in Mathlib
Foundations
Depth 7 from the axioms, rests on 18 definitions · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct

Around this declaration

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

CategoryTheory.Limits.biprod.hom_ext · cited by 34biprod.hom_extCategoryTheory.Limits.biprod.lift_snd · cited by 33biprod.lift_sndCategoryTheory.kernelCokernelCompSequence.snakeInput · cited by 31kernelCokernelCompSequenc…HomologicalComplex.homotopyCofiber.sndX · cited by 27homotopyCofiber.sndXCategoryTheory.Pretriangulated.binaryBiproductTriangle · cited by 14Pretriangulated.binaryBip…CategoryTheory.Functor.biprodComparison · cited by 11Functor.biprodComparisonCategoryTheory.Biprod.ofComponents · cited by 10Biprod.ofComponentsCategoryTheory.Limits.pointwiseBinaryBicone · cited by 9Limits.pointwiseBinaryBic…CategoryTheory.Limits.biprod.braiding · cited by 9biprod.braidingHomologicalComplex.homotopyCofiber.inrX_sndX · cited by 8homotopyCofiber.inrX_sndXCategoryTheory.Limits.biprod.lift_desc · cited by 7biprod.lift_descHomologicalComplex.homotopyCofiber.inlX_sndX · cited by 6homotopyCofiber.inlX_sndXCategoryTheory.Limits.biprod.associator · cited by 6biprod.associatorCategoryTheory.Limits.biprod.map_snd · cited by 5biprod.map_sndHomologicalComplex.homotopyCofiber.ext_to_X · cited by 5homotopyCofiber.ext_to_XCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.biprod · cited by 312Limits.biprodCategoryTheory.Limits.HasBinaryBiproduct · cited by 251Limits.HasBinaryBiproductCategoryTheory.Limits.BinaryBiproduct.bicone · cited by 68BinaryBiproduct.biconeCategoryTheory.Limits.BinaryBicone.snd · cited by 48BinaryBicone.sndbiprod.sndCITED BYCITES

Cites7

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Cited by156

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