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 ⟶ YThe projection onto the second summand of a binary biproduct.
- Cited by
- 132 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 18 definitions · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Limits.biprodstatement · cited by 312
- CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
- CategoryTheory.Limits.BinaryBiproduct.biconeproof · cited by 68
- CategoryTheory.Limits.BinaryBicone.sndproof · cited by 48
Cited by156
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.biprod.hom_extstatement and proof · cited by 34
- CategoryTheory.Limits.biprod.lift_sndstatement · cited by 33
- CategoryTheory.kernelCokernelCompSequence.snakeInputproof · cited by 31
- HomologicalComplex.homotopyCofiber.sndXproof · cited by 27
- CategoryTheory.Pretriangulated.binaryBiproductTriangleproof · cited by 14
- CategoryTheory.Functor.biprodComparisonproof · cited by 11
- CategoryTheory.Biprod.ofComponentsproof · cited by 10
- CategoryTheory.Limits.pointwiseBinaryBiconeproof · cited by 9
- CategoryTheory.Limits.biprod.braidingproof · cited by 9
- HomologicalComplex.homotopyCofiber.inrX_sndXproof · cited by 8
- CategoryTheory.Limits.biprod.lift_descproof · cited by 7
- HomologicalComplex.homotopyCofiber.inlX_sndXproof · cited by 6