Theorems · Definition · category theory
CategoryTheory.Limits.limit.isoLimitCone
{J : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} J] →
{C : Type u} →
[inst_1 : CategoryTheory.Category.{v, u} C] →
{F : CategoryTheory.Functor J C} →
[inst_2 : CategoryTheory.Limits.HasLimit F] →
(t : CategoryTheory.Limits.LimitCone F) → CategoryTheory.Limits.limit F ≅ t.cone.ptGiven any other limit cone for F, the chosen limit F is isomorphic to the cone point.
- Defined in
- Mathlib.CategoryTheory.Limits.HasLimits
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Cone.ptstatement · cited by 1,298
- CategoryTheory.Limits.limitstatement · cited by 346
- CategoryTheory.Limits.HasLimitstatement and proof · cited by 226
- CategoryTheory.Limits.limit.isLimitproof · cited by 146
- CategoryTheory.Limits.LimitCone.conestatement · cited by 72
- CategoryTheory.Limits.LimitCone.isLimitproof · cited by 58
- CategoryTheory.Limits.IsLimit.conePointUniqueUpToIsoproof · cited by 57
- CategoryTheory.Limits.LimitConestatement and proof · cited by 25
Cited by36
Results whose statement or proof uses this declaration.
- CategoryTheory.IsPullback.isoPullbackproof · cited by 42
- CategoryTheory.Limits.limit.isoLimitCone_inv_πstatement · cited by 26
- AlgebraicGeometry.pullbackSpecIsoproof · cited by 26
- prodIsoPullbackproof · cited by 13
- CategoryTheory.Limits.Types.binaryProductIsoproof · cited by 10
- CategoryTheory.Limits.Types.productIsoproof · cited by 9
- CategoryTheory.Limits.limit.isoLimitCone_hom_πstatement · cited by 8
- CategoryTheory.Limits.Types.equalizerIsoproof · cited by 7
- CategoryTheory.FunctorToTypes.binaryProductIsoproof · cited by 7
- CategoryTheory.Limits.Types.Small.productIsoproof · cited by 6
- CategoryTheory.Limits.pullbackZeroZeroIsoproof · cited by 5
- CategoryTheory.Limits.limitOpIsoOpColimitproof · cited by 5