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Theorems · Definition · category theory

CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial

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

The (unique) isomorphism between any initial object and the zero object.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects
Cited by
2 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObject
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Around this declaration

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

CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_hom · cited by 0HasZeroObject.zeroIsoIsIn…CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_inv · cited by 0HasZeroObject.zeroIsoIsIn…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectCategoryTheory.Limits.IsInitial · cited by 158Limits.IsInitialCategoryTheory.Limits.HasZeroObject.zero' · cited by 115HasZeroObject.zero'CategoryTheory.Limits.IsInitial.uniqueUpToIso · cited by 8IsInitial.uniqueUpToIsoCategoryTheory.Limits.HasZeroObject.zeroIsInitial · cited by 5HasZeroObject.zeroIsIniti…HasZeroObject.zeroIsoIsInitialCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.