Theorems · Definition · category theory

CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] → [inst_2 : CategoryTheory.Limits.HasTerminal C] → 0 ≅ ⊤_ C

The (unique) isomorphism between the chosen terminal object and the chosen zero object.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects
Cited by: 3 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasTerminal

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

Cites9

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.HasTerminalstatement and proof · cited by 142
CategoryTheory.Limits.terminalstatement · cited by 141
CategoryTheory.Limits.HasZeroObject.zero'statement · cited by 115
CategoryTheory.Limits.terminalIsTerminalproof · cited by 31
CategoryTheory.Limits.IsTerminal.uniqueUpToIsoproof · cited by 10
CategoryTheory.Limits.HasZeroObject.zeroIsTerminalproof · cited by 4

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.preservesTerminalObject_of_preservesZeroMorphismsproof · cited by 1
CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_homstatement and proof · cited by 0
CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_invstatement and proof · cited by 0