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Theorems · Definition · category theory

CategoryTheory.Limits.IsTerminal.ofUniqueHom

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {Y : C} → (h : (X : C) → X ⟶ Y) → (∀ (X : C) (m : X ⟶ Y), m = h X) → CategoryTheory.Limits.IsTerminal Y

An object Y is terminal if for every X there is a unique morphism X ⟶ Y (as explicit arguments).

Defined in
Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
Cited by
5 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.Over.cartesianMonoidalCategory · cited by 68Over.cartesianMonoidalCat…CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryOver · cited by 49ChosenPullbacksAlong.cart…CategoryTheory.Limits.FormalCoproduct.isTerminalIncl · cited by 9FormalCoproduct.isTermina…CategoryTheory.Functor.isTerminalConst · cited by 8Functor.isTerminalConstCategoryTheory.Sheaf.isTerminalTerminal · cited by 4Sheaf.isTerminalTerminalCategoryTheory.Over.rightUnitor_inv_left_fst · cited by 2Over.rightUnitor_inv_left…CategoryTheory.Limits.IsInitial.op · cited by 2IsInitial.opCategoryTheory.SubobjectRepresentableBy.isTerminalΩ₀ · cited by 1SubobjectRepresentableBy.…CategoryTheory.Over.rightUnitor_inv_left_snd · cited by 1Over.rightUnitor_inv_left…SSet.stdSimplex.isTerminalObj₀ · cited by 1stdSimplex.isTerminalObj₀CategoryTheory.Over.leftUnitor_inv_left_fst · cited by 1Over.leftUnitor_inv_left_…CategoryTheory.Over.leftUnitor_inv_left_snd · cited by 1Over.leftUnitor_inv_left_…CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.isUniversal · cited by 1IsPointwiseRightKanExtens…CategoryTheory.Limits.IsInitial.unop · cited by 0IsInitial.unopCategoryTheory.Cat.chosenTerminalIsTerminal · cited by 0Cat.chosenTerminalIsTermi…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomUnique · cited by 400UniqueCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalCategoryTheory.Limits.IsTerminal.ofUnique · cited by 0IsTerminal.ofUniqueIsTerminal.ofUniqueHomCITED BYCITES

Cites5

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Cited by19

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