Theorems · Definition · category theory

CategoryTheory.Limits.IsZero.isoZero

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] → {X : C} → CategoryTheory.Limits.IsZero X → (X ≅ 0)

Every zero object is isomorphic to the zero object.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects
Cited by: 7 results in Mathlib
Foundations: Depth 11 from the axioms · uses Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject

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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
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.Limits.IsZerostatement and proof · cited by 306
CategoryTheory.Limits.HasZeroObject.zero'statement · cited by 115
CategoryTheory.Limits.isZero_zeroproof · cited by 34
CategoryTheory.Limits.IsZero.isoproof · cited by 11

Cited by7

Results whose statement or proof uses this declaration.

CategoryTheory.Pretriangulated.Triangle.distinguished_iff_of_isZero₃proof · cited by 2
TopCat.Sheaf.isZero_iff_stalkFunctor_obj_isZeroproof · cited by 1
CategoryTheory.Limits.isIsoZero_iff_source_target_isZeroproof · cited by 1
CategoryTheory.Triangulated.TStructure.isLE_of_isZeroproof · cited by 1
CategoryTheory.Triangulated.TStructure.isGE_of_isZeroproof · cited by 1
CategoryTheory.ShortComplex.exact_iff_homology_iso_zeroproof · cited by 0
HomotopyCategory.Pretriangulated.contractible_distinguishedproof · cited by 0