Theorems · Definition · category theory
CategoryTheory.Limits.IsLimit.uniqueUpToIso
{J : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} J] →
{C : Type u₃} →
[inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
{F : CategoryTheory.Functor J C} →
{s t : CategoryTheory.Limits.Cone F} →
CategoryTheory.Limits.IsLimit s → CategoryTheory.Limits.IsLimit t → (s ≅ t)Limit cones on F are unique up to isomorphism.
- Defined in
- Mathlib.CategoryTheory.Limits.IsLimit
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Functorstatement and proof · cited by 16,252
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Limits.Conestatement and proof · cited by 710
- CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
- CategoryTheory.Limits.IsLimit.liftConeMorphismproof · cited by 18
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsLimit.conePointUniqueUpToIsoproof · cited by 57
- CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_inv_compproof · cited by 37
- CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_compproof · cited by 33
- CategoryTheory.Limits.preservesLimit_of_preserves_limit_coneproof · cited by 22
- CategoryTheory.Limits.IsLimit.uniqueUpToIso_homstatement and proof · cited by 2
- CategoryTheory.Limits.IsLimit.uniqueUpToIso_invstatement and proof · cited by 1
- CategoryTheory.Limits.kernel.ofMonoproof · cited by 1
- CategoryTheory.Functor.PreservesPointwiseRightKanExtensionAt.mk'proof · cited by 0
- CategoryTheory.createsLimitOfNatIsoproof · cited by 0
- CategoryTheory.createsLimitOfReflectsIso'proof · cited by 0