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Theorems · Definition · category theory

CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal

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

The (unique) isomorphism between any terminal 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.zeroIsoIsTerminal_hom · cited by 0HasZeroObject.zeroIsoIsTe…CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_inv · cited by 0HasZeroObject.zeroIsoIsTe…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalCategoryTheory.Limits.HasZeroObject.zero' · cited by 115HasZeroObject.zero'CategoryTheory.Limits.IsTerminal.uniqueUpToIso · cited by 10IsTerminal.uniqueUpToIsoCategoryTheory.Limits.HasZeroObject.zeroIsTerminal · cited by 4HasZeroObject.zeroIsTermi…HasZeroObject.zeroIsoIsTermin…CITED 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.