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Theorems · Definition · category theory

CategoryTheory.Limits.HasZeroObject.zeroIsTerminal

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

A zero object is in particular terminal.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects
Cited by
4 results in Mathlib
Foundations
Depth 27 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.pullbackZeroZeroIso · cited by 5Limits.pullbackZeroZeroIsoCategoryTheory.IsPullback.of_isBilimit · cited by 4IsPullback.of_isBilimitCategoryTheory.Limits.HasZeroObject.zeroIsoTerminal · cited by 3HasZeroObject.zeroIsoTerm…CategoryTheory.Limits.pullbackZeroZeroIso_inv_fst · cited by 2Limits.pullbackZeroZeroIs…CategoryTheory.Limits.pullbackZeroZeroIso_inv_snd · cited by 2Limits.pullbackZeroZeroIs…CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal · cited by 2HasZeroObject.zeroIsoIsTe…CategoryTheory.IsPullback.of_hasBinaryProduct · cited by 0IsPullback.of_hasBinaryPr…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalCategoryTheory.Limits.HasZeroObject.zero' · cited by 115HasZeroObject.zero'CategoryTheory.Limits.isZero_zero · cited by 34Limits.isZero_zeroCategoryTheory.Limits.IsZero.isTerminal · cited by 0IsZero.isTerminalHasZeroObject.zeroIsTerminalCITED BYCITES

Cites6

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Cited by7

Results whose statement or proof uses this declaration.