Theorems · Definition · category theory

CategoryTheory.Limits.IsZero.iso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} → CategoryTheory.Limits.IsZero X → CategoryTheory.Limits.IsZero Y → (X ≅ Y)

Any two zero objects are isomorphic.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects
Cited by: 11 results in Mathlib
Foundations: Depth 10 from the axioms · uses Classical.choice
Assumes: CategoryTheory.Category

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

Cites5

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
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Limits.IsZerostatement and proof · cited by 306
CategoryTheory.Limits.IsZero.from_proof · cited by 8
CategoryTheory.Limits.IsZero.to_proof · cited by 8

Cited by14

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.IsZero.isoZeroproof · cited by 7
CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIsoproof · cited by 7
AddCommGrpCat.subsingleton_of_isZeroproof · cited by 4
CategoryTheory.Limits.IsZero.objproof · cited by 3
CategoryTheory.ObjectProperty.prop_of_isZeroproof · cited by 3
HomologicalComplex.extend.XOpIsoproof · cited by 2
CommGrpCat.subsingleton_of_isZeroproof · cited by 1
GrpCat.subsingleton_of_isZeroproof · cited by 1
AddGrpCat.subsingleton_of_isZeroproof · cited by 1
CategoryTheory.ObjectProperty.le_extensionProduct_rightproof · cited by 1
CategoryTheory.Limits.IsZero.iso.congr_simpstatement and proof · cited by 0
CategoryTheory.ObjectProperty.le_extensionProduct_leftproof · cited by 0