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Theorems · Definition · category theory

CategoryTheory.Limits.IsTerminal.uniqueUpToIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {T T' : C} → CategoryTheory.Limits.IsTerminal T → CategoryTheory.Limits.IsTerminal T' → (T ≅ T')

If T and T' are terminal, they are isomorphic.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
Cited by
10 results in Mathlib
Foundations
Depth 30 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.MonoidalCategory.Arrow.PushoutProduct.isInitialIsTerminalIso · cited by 4PushoutProduct.isInitialI…CategoryTheory.Limits.terminalIsoIsTerminal · cited by 4Limits.terminalIsoIsTermi…CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal · cited by 3HasZeroObject.zeroIsoTerm…CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal · cited by 2HasZeroObject.zeroIsoIsTe…HomotopicalAlgebra.isFibrant_iff_of_isTerminal · cited by 2HomotopicalAlgebra.isFibr…SSet.Truncated.HomotopyCategory.isoTerminal · cited by 2HomotopyCategory.isoTermi…CategoryTheory.WithTerminal.starIsoTerminal · cited by 2WithTerminal.starIsoTermi…CategoryTheory.Bicategory.RightLift.IsKan.uniqueUpToIso · cited by 2IsKan.uniqueUpToIsoAlgebraicGeometry.Scheme.nonempty_of_isLimit · cited by 1Scheme.nonempty_of_isLimitCategoryTheory.Limits.IsTerminal.uniqueUpToIso_hom · cited by 1IsTerminal.uniqueUpToIso_…CategoryTheory.IsSifted.nonempty_of_colim_preservesLimitsOfShapeFinZero · cited by 1IsSifted.nonempty_of_coli…CategoryTheory.Limits.Types.terminalIso · cited by 1Types.terminalIsoCategoryTheory.Limits.IsZero.isoIsTerminal · cited by 0IsZero.isoIsTerminalCategoryTheory.Functor.PreservesRightKanExtension.mk_of_preserves_isUniversal · cited by 0PreservesRightKanExtensio…TopCat.terminalIsoPUnit · cited by 0TopCat.terminalIsoPUnitCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.IsTerminal.from · cited by 160IsTerminal.fromCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalIsTerminal.uniqueUpToIsoCITED BYCITES

Cites4

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Cited by23

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